Recent questions in Differential Equations

Verify that the given function(explicit or implicit)is a solution of the corresponding differential equation\[y=\sqrt{1+x^2}\qquad:\;y'\;=\frac{xy}{1+x^2}\]

asked Nov 30, 2012 by sreemathi.v

1 answer

Verify that the given function(explicit or implicit)is a solution of the corresponding differential equation $y=Ax\qquad:\;xy'\;=\;y\;(x\neq0)$

asked Nov 30, 2012 by sreemathi.v

1 answer

Verify that the given function(explicit or implicit)is a solution of the corresponding differential equation $y=x\sin x\qquad:xy'=y+x\sqrt{x^2-y^2} (x\neq0\;and\;x>y\;or\;x<-y)$

asked Nov 30, 2012 by sreemathi.v

1 answer

Verify that the given function(explicit or implicit)is a solution of the corresponding differential equation $xy=\log\: y+C\qquad:y'=\large\frac{y^2}{1-xy}$$\;(xy\neq1)$

asked Nov 30, 2012 by sreemathi.v

1 answer

Verify that the given function(explicit or implicit)is a solution of the corresponding differential equation $y-\cos y=x\qquad:\;(y\sin y+\cos y+x)y'=y$

asked Nov 30, 2012 by sreemathi.v

1 answer

Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation

asked Nov 30, 2012 by sreemathi.v

1 answer

Verify that the given function(explicit or implicit)is a solution of the corresponding differential equation $y=\sqrt{a^2-x^2}\;x\in\;(-a,a):\;x+y\;\large\frac{dy}{dx}$$=0(y\neq0)$

asked Nov 30, 2012 by sreemathi.v

1 answer

The number of arbitrary constants in the general solution of a differential equation of fourth order are

asked Nov 30, 2012 by sreemathi.v

1 answer

The number of arbitrary constants in the particular solution of a differential equation of third order are

asked Nov 30, 2012 by sreemathi.v

1 answer

Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b $\large\frac{x}{a}+\frac{y}{b}=1$

asked Nov 30, 2012 by sreemathi.v

1 answer

Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.$y^2=a(b^2-x^2)$

asked Nov 30, 2012 by sreemathi.v

1 answer

Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b. $y=a\: e^{3x}+b\: e^{-2x}$

asked Nov 30, 2012 by sreemathi.v

1 answer

Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b $y=e^{2x}(a+bx)$

asked Nov 30, 2012 by sreemathi.v

1 answer

Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b $y=e^x(a\;\cos x+b\;\sin x)$

asked Nov 30, 2012 by sreemathi.v

1 answer

Form the differential equation of the family of circles touching the $y$ - axis at origin.

asked Nov 30, 2012 by sreemathi.v

1 answer

Form the differential equation of the family of parabolas having vertex at origin at axis along positive y-axis.

asked Nov 30, 2012 by sreemathi.v

1 answer

Form the differential equation of the family of ellipses having foci on $y$-axis and centre at origin.

asked Nov 30, 2012 by sreemathi.v

1 answer

Form the differential equation of the family of hyperbolas having foci on $x$-axis and centre at origin.

asked Nov 30, 2012 by sreemathi.v

1 answer

Form the differential equation of the family of circles having centre on $y$-axis and radius $3$ units.

asked Nov 30, 2012 by sreemathi.v

2 answers

Which of the following differential equations has $y\;=\;c_1e^x+c_2e^{-x}$ as the general solution?

asked Nov 30, 2012 by sreemathi.v

1 answer

Which of the following differential equations has $y = x$ as one of its particular solution?

asked Nov 30, 2012 by sreemathi.v

1 answer

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

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the general solution $\large\frac{dy}{dx} $$=\sqrt {4-y^2} \; (-2\lt y \lt 2) $

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the general solution $\large\frac{dy}{dx}$$+y=1(y\neq1)$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the general solution $\sec^2x\;\tan y\;dx+\sec^2y\;\tan x\;dy=0$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the general solution $(e^x+e^{-x})\;dy-(e^x-e^{-x})\;dx=0$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the general solution $\large\frac{dy}{dx}$$=(1+x^2)(1+y^2)$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the general solution $y\;\log\: y\;dx-x\;dy=0$

asked Nov 30, 2012 by sreemathi.v

1 answer

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

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