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Recent questions tagged ch9

Find the general solution $x^5\large\frac{dy}{dx}$$=-y^5$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the general solution $\large\frac{dy}{dx}=$$\sin^{-1}x$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the general solution $e^x\tan y\;dx+(1-e^x)\sec ^2y\;dy=0$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find a particular solution satisfying the given condition $(x^3+x^2+x+1)\large\frac{dy}{dx}$$=2x^2+x;y=1\;when\;x=0$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find a particular solution satisfying the given condition $x(x^2-1)\large\frac{dy}{dx}$$=1;y=0\;when\;x=2$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find a particular solution satisfying the given condition $\cos\bigg(\large\frac{dy}{dx}\bigg)$$=a\;(a\;\in\;R);y=2\;when\;x=0$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find a particular solution satisfying the given condition$\large\frac{dy}{dx}=$$y\tan x;\;y=1\;when\;x=0$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the equation of a curve passing through the point $(0,0)$ and whose differential equation is $y'=e^x\;\sin x.$

asked Nov 30, 2012 by sreemathi.v

1 answer

For the differential equation $xy\large\frac{dy}{dx}=$$(x+2)(y+2),$ find the solution curve passing through the point $(1,-1)$.

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the equation of a curve passing through the point (0,-2) given that at any point (x,y) on the curve,the product of the slope of its tangent and y coordinate of the point is equal to the x coordinate of the point.

asked Nov 30, 2012 by sreemathi.v

1 answer

At any point (x,y) of a curve,the slope of the tangent is twice the slope of the line segment joining the point of contact to the point (-4,-3).Find the equation of the curve given that it passes through (-2,1).

asked Nov 30, 2012 by sreemathi.v

1 answer

In a bank,principal increases continuously at the rate of r% per year.Find the value of r if Rs100 doubles itself in 10years. $\quad (log_e2=0.6931)$

asked Nov 30, 2012 by sreemathi.v

1 answer

The volume of spherical balloon being inflated changes at a constant rate.If initially its radius is 3units and after 3seconds it is 6units.Find the radius of balloon after t seconds.

asked Nov 30, 2012 by sreemathi.v

1 answer

In a bank, principal increases continuously at the rate of $5\%$ per year. An amount of $Rs.1000$ is deposited with this bank, how much will it work after $10$ years $(e^{0.5}=1.648)$.

asked Nov 30, 2012 by sreemathi.v

1 answer

In a culture, the bacteria count is $1,00,000.$ The number is increased by $10\%$ in $2$hours.In how many hours will the count reach $2,00,000$ if the rate of growth of bacteria is proportional to the number present?

asked Nov 30, 2012 by sreemathi.v

1 answer

The general solution of the differential equation\(\frac{\large dy}{\large dx}=e^{x+y}\)is

asked Nov 30, 2012 by sreemathi.v

1 answer

Show that the differential equation is homogeneous and solve $(x^2+xy)\;dy=(x^2+y^2)\;dx$

asked Nov 30, 2012 by sreemathi.v

1 answer

Show that the differential equation is homogeneous and solve\[y'=\frac{x+y}{x}\]

asked Nov 29, 2012 by sreemathi.v

1 answer

Show that the differential equation is homogeneous and solve\[(x-y)\;dy-(x+y)\;dx=0\]

asked Nov 29, 2012 by sreemathi.v

1 answer

Show that the differential equation is homogeneous and solve $(x^2-y^2)dx+2xy\;dy=0$

asked Nov 29, 2012 by sreemathi.v

1 answer

Show that the differential equation is homogeneous and solve $x^2\large\frac{dy}{dx}$$=x^2-2y^2+xy$

asked Nov 29, 2012 by sreemathi.v

1 answer

Show that the differential equation is homogeneous and solve $x\;dy-y\;dx=\sqrt{x^2+y^2}dx$

asked Nov 29, 2012 by sreemathi.v

1 answer

Show that the differential equation is homogeneous and solve $\left\{x\cos\bigg(\large\frac{y}{x}\bigg)\normalsize+y\sin\bigg(\large\frac{y}{x}\bigg)\right\}ydx=\left\{y\sin\bigg(\large\frac{y}{x}\bigg)-\normalsize x\cos\bigg(\large\frac{y}{x}\bigg)\right\}\normalsize xdy$

asked Nov 29, 2012 by sreemathi.v

1 answer

Show that the differential equation is homogeneous and solve $x\large\frac{dy}{dx}$$-y+x\sin\bigg(\large\frac{y}{x}\bigg)=$$0$

asked Nov 29, 2012 by sreemathi.v

1 answer

Show that the differential equation is homogeneous and solve $y\: dx+x\log\bigg(\large\frac{y}{x}\bigg)$$dy-2x\;dy=0$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the particular solution satisfying the given condition $(x+y)dy+(x-y)dx=0;\;y=1;\;when\;x=\;1$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the particular solution satisfying the given condition $x^2dy+(xy+y^2)\;dx=0;y=\;1;\;when\;x=\;1$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the particular solution satisfying the given condition $\large\frac{dy}{dx}-\large\frac{y}{x}$$+cosec\bigg(\large\frac{y}{x}\bigg)$$=0;\;y=\;0\;when\;x=\;1$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the particular solution satisfying the given condition $2xy+y^2-2x^2\large\frac{dy}{dx}$$=0;\;y=\;2\;when\;x=\;1$

asked Nov 29, 2012 by sreemathi.v

1 answer

A homogeneous differential equation of the form $\frac{\large dx}{\large dy}=h\bigg(\frac{\large x}{\large y}\bigg)$ can be solved by making the substitution

asked Nov 29, 2012 by sreemathi.v

1 answer

Which of the following is a homogeneous differential equation?

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the general solution of the differential equation $\large\frac{dy}{dx}$$+2y=\sin x$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the general solution of the differential equation$\large\frac{dy}{dx}$$+3y=e^{-2x}$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the general solution of the differential equation$\large\frac{dy}{dx}+\frac{y}{x}$$=x^2$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the general solution of the differential equation$\large\frac{dy}{dx}$$+(\sec x)y=\tan x\bigg(0\leq x<\large\frac{\pi}{2}\bigg)$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the general solution of the differential equation $\cos^2x\large\frac{dy}{dx}$$+y=\tan x\bigg(0\leq x<\large\frac{\pi}{2}\bigg)$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the general solution of the differential equation $x\large\frac{dy}{dx}$$+2y=x^2\log x$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the general solution of the differential equation $x \log x\large\frac{dy}{dx}$$+y=\large\frac{2}{x}$$\log x$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the general solution of the differential equation $(1+x^2)dy+2xy\;dx=\cot x\;dx\;(x\neq0)$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the general solution of the differential equation $x\large\frac{dy}{dx}$$+y-x+xy\cot x=0\;(x\neq0)$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the general solution of the differential equation $(x+y)\large\frac{dy}{dx}$$=1$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the general solution of the differential equation $y\;dx+(x-y^2)dy=0$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the general solution of the differential equation $(x+3y^2)\large\frac{dy}{dx}=y$$\;(y>0)$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find a particular solution satisfying the given condition$\large\frac{dy}{dx}$$+2y\tan x=\sin x;\;y=o\;when\;x=\large\frac{\pi}{3}$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find a particular solution satisfying the given condition $(1+x^2)\large\frac{dy}{dx}$$+2xy=\large\frac{1}{1+x^2}$$;y=0\;when\;x=1$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find a particular solution satisfying the given condition $\large\frac{dy}{dx}-$$3y\cot x=\sin 2x;\;y=2\;when\;x=\large\frac{\pi}{2}$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the equation of curve passing through the origin given that the slope of the tangent to the curve at any point \((x,y)\) is equal to the sum of the coordinates of the point .

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the equation of curve passing through the point(0,2) given that the sum of the coordinates of any point on the curve exceeds the magnitude of the slope of the tangent to the curve at that point by 5

asked Nov 29, 2012 by sreemathi.v

1 answer

The integrating factor of the differential equation $x\large\frac{dy}{dx}$$-y=2x^2 $ is

asked Nov 29, 2012 by sreemathi.v

1 answer

The integrating factor of the differential equation $(1-y^2)\large\frac{dx}{dy}$$+yx=ay\: \;is$

asked Nov 29, 2012 by sreemathi.v

1 answer

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