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Questions >> TN XII Math >> Differential Equations

Differential equation - Linear

asked Nov 20, 2014 by govindan.abhilash

2 answers

Homogeneous equation

asked Nov 16, 2014 by govindan.abhilash

1 answer

Solve the following differential equation; $(D^{2}-13D+12)$ y $=e^{-2x}+5e^x$

asked Sep 5, 2013 by sreemathi.v

1 answer

A radioactive substance disintegrates at a rate proportional to its mass. When its mass is $10$ mgm, the rate of disintegration is $0.051$ mgm per day. How long will it take for the mass to be reduced from $10$ mgm to $5$ mgm. $[\log_{e}$ $2=0.6931]$

asked Apr 17, 2013 by poojasapani_1

1 answer

The rate at which the population of a city increases at any time is propotional to the population at that time. If there were $1,30,000$ people in the city in $1960$ and $1,60,000$ in $1990$ what population may be anticipated in $2020$ . $[\log_{e}(\large\frac{16}{13})=$ $.2070;$ $e^{.42}=1.52]$

asked Apr 17, 2013 by poojasapani_1

1 answer

A cup of coffee at temperature $100^{\circ}$ $C$ is placed in a room whose temperature is $15^ {\circ}$ $C$ and it cools to $60^{\circ}$ $C$ in $5$ minutes . Find its temperature after a further interval of $5$ minutes.

asked Apr 17, 2013 by poojasapani_1

1 answer

The sum of Rs $1000$ is compounded continuously, the nominal rate of interest being four percent per annum. In how many years will the amount be twice the original principal ? $(\log_{e}$ $2=0.6931)$

asked Apr 17, 2013 by poojasapani_1

1 answer

Radium disappears at a rate propotional to the amount present .If $5\%$ of the original amount disappears in $50$ years , how much will remain at the end of $100$ years [Take $A_{0}$ as a intial amount.]

asked Apr 17, 2013 by poojasapani_1

1 answer

Solve the following differential equation; $(3D^{2}+4D+1)$ $y=3e^{-\Large\frac{x}{3}}$

asked Apr 16, 2013 by poojasapani_1

1 answer

Solve the following differential equation; $(D^{2}+2D+3)$ $y=\sin$ $2x$

asked Apr 16, 2013 by poojasapani_1

1 answer

Solve the following differential equation; $(D^{2}+5)$ $y=\cos^{2}$ $x$

asked Apr 16, 2013 by poojasapani_1

1 answer

Solve the following differential equation; $(D^{2}-1)$ $y=\cos$ $2x-2\sin$ $2x$

asked Apr 16, 2013 by poojasapani_1

1 answer

Solve the following differential equation; $(D^{2}-6D+9)$ $y=x+e^{2x}$

asked Apr 16, 2013 by poojasapani_1

1 answer

Solve the following differential equation; $D^{2}$ $y=-9\sin$ $3x$

asked Apr 16, 2013 by poojasapani_1

1 answer

Solve the following differential equation; $(D^{2}-2D-3)$ $y=\sin$ $x\cos$ $x$

asked Apr 16, 2013 by poojasapani_1

1 answer

Solve the following differential equation; $(D^{2}+3D-4)$ $y=x^{2}$

asked Apr 16, 2013 by poojasapani_1

1 answer

Solve the following differential equation; $\large\frac{d^{2}y}{dx^{2}}$ $-3\large\frac{dy}{dx}$ $+2y=2e^{3x}$ when $x =\log$ $2$ , $y=0,$ and when $x=0,y=0$

asked Apr 16, 2013 by poojasapani_1

1 answer

Solve the following differential equation; $(D^{2}+1)$ Y= $0$ when $x=0;y=2$ and when $x=\large\frac{\pi}{2};$ $y=-2$

asked Apr 16, 2013 by poojasapani_1

1 answer

Solve the following differential equation; $(D^{2}+14D+49)$ y $=e^{-7x}+4$

asked Apr 16, 2013 by poojasapani_1

1 answer

Solve the following differential equation; $(D^{2}-4D+13)$ y $=e^{-3x}$

asked Apr 16, 2013 by poojasapani_1

1 answer

Solve the following differential equation; $(D^{2}+7D+12)$ y $=e^{2x}$

asked Apr 16, 2013 by poojasapani_1

1 answer

Show that the equation of the curve whose slope at any point is equal to $y+2x$ and which passes through the origin is $y\;=\;2(e^{x}-x-1)$

asked Apr 16, 2013 by poojasapani_1

1 answer

Solve the following. $(y - x)\large\frac{dy}{dx}$ = $a^{2}$

asked Apr 16, 2013 by poojasapani_1

1 answer

Solve the following. $dx+x\;dy=e^{-y}\;\sec^{2}y\;dy$

asked Apr 16, 2013 by poojasapani_1

1 answer

Solve the following. $\large\frac{dy}{dx}$ $+xy\;=\;x$

asked Apr 16, 2013 by poojasapani_1

1 answer

Solve the following. $\large\frac{dy}{dx}+\frac{y}{x}$ $\;=\;\sin(x^{2})$

asked Apr 16, 2013 by poojasapani_1

1 answer

Solve the following. $(1+x^{2}) \large\frac{dy}{dx}$ $+2xy\;=\; \cos$ $x$

asked Apr 16, 2013 by poojasapani_1

1 answer

Solve the following. $\large\frac{dx}{dy}=\frac{x}{1+y^2}=\frac{\tan^{-1}}{1+y^2}$

asked Apr 16, 2013 by poojasapani_1

1 answer

Solve the following. $\large\frac{dy}{dx}+\frac{4x}{x^{2}+1}$ $y=\large \frac{1}{(x^{2}+1)^{2}}$

asked Apr 16, 2013 by poojasapani_1

1 answer

Solve the following. $\large\frac{dy}{dx}$ $+y\;=\;x$

asked Apr 16, 2013 by poojasapani_1

1 answer

Find the equation of the curve passing through $(1 , 0 )$ and which has slope $1+\large\frac{y}{x}$ at $(x , y )$

asked Apr 15, 2013 by poojasapani_1

1 answer

Solve the following $(x^{2}+y^{2})dx+3xy dy$ = $0$

asked Apr 15, 2013 by poojasapani_1

1 answer

Solve the following $x^{2}\large\frac{dy}{dx}$ = $y^{2}+2xy$ given that $y=1,$ when $x=1$

asked Apr 15, 2013 by poojasapani_1

1 answer

Solve the following $\large\frac{dy}{dx}$ = $\large\frac {y(x-2y)}{x(x-3y)}$

asked Apr 15, 2013 by poojasapani_1

1 answer

Solve the following $(x^{2}+y^{2})\;dy$ = $xy \;dx$

asked Apr 15, 2013 by poojasapani_1

1 answer

Solve the following $\large\frac{dy}{dx}+\frac{y}{x}=\frac{y^{2}}{x^{2}}$

asked Apr 15, 2013 by poojasapani_1

1 answer

Solve the following $ydx +xdy=e^{-xy}\;dx$ if it cuts the Y- axis.

asked Apr 15, 2013 by poojasapani_1

1 answer

Solve the following $(x+y)^2 \large\frac{dy}{dx}$ = $1$

asked Apr 15, 2013 by poojasapani_1

1 answer

Solve the following $\large\frac{dy}{dx}$ $=\sin(x+y)$

asked Apr 15, 2013 by poojasapani_1

1 answer

Solve the following $(x^{2}+5x+7) dy+\sqrt{9+8y-y^{2}}dx=0$

asked Apr 15, 2013 by poojasapani_1

1 answer

Solve the following $yx^{2}dx+e^{-x}dy=0$

asked Apr 15, 2013 by poojasapani_1

1 answer

Solve the following $(x^{2}-yx^{2})dy+(y^{2}+xy^{2})dx=0$

asked Apr 15, 2013 by poojasapani_1

1 answer

Solve the following $\cos^{2}xdy +ye^{\tan x }dx=0$

asked Apr 15, 2013 by poojasapani_1

1 answer

Solve the following $\sec 2x dy -\sin 5x \sec^{2} ydx=0$

asked Apr 15, 2013 by poojasapani_1

1 answer

Find the differential equation that will represent the family of all circles having centres on the X-axis and the radius is unity.

asked Apr 15, 2013 by poojasapani_1

1 answer

Find the differential equation of family of straight lines $y=mx+\large\frac{a}{m}$ When $a , m,$ both are parameters.

asked Apr 15, 2013 by poojasapani_1

1 answer

Find the differential equation of family of straight lines $y=mx+\large\frac{a}{m}$ When $a$ is the parameter.

asked Apr 15, 2013 by poojasapani_1

1 answer

Find the differential equation of family of straight lines $y=mx+\large\frac{a}{m}$ When $m$ is the parameter.

asked Apr 15, 2013 by poojasapani_1

1 answer

Form the differential equuations by eliminating arbitary constants given in brackets against each. $y=Ae^{2x} \cos (3x , +B ) [A , B ]$

asked Apr 15, 2013 by poojasapani_1

1 answer

Form the differential equuations by eliminating arbitary constants given in brackets against each $y=e^{mx} [m]$

asked Apr 15, 2013 by poojasapani_1

1 answer

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