Class 12

Math

Calculus

Differential Equations

The differential equation whose general solution is given by $y=c_{1}cos(x+c_{2})−c_{3}e_{−x+c_{4}}+c_{5}sinx$, where $c_{1},c_{2},c_{3},c_{4},c_{5}$ are arbitary constants, is

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Find the general solution of the differential equations:$dydx +secxy=tanx(0≤x<2π )$

If $y(x)$ satisfies the differential equation $dxdy =xx_{2}−2y $ where \displaystyle{y}

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Find a particular solution of the differential equation$(x−y)(dx+dy)=dxdy$, given that $y=1$, when $x=0$. (Hint: put $x−y=t$).

The general solution of the differential equation $yydx−xdy =0$is(A) $xy=C$ (B) $x=Cy_{2}$ (C) $y=Cx$ (D) $y=Cx_{2}$

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Verify that the function $y=e_{−3x}$is a solution of the differential equation $dx_{2}d_{2}y +dxdy −6y=0$

Let $y(x)$ be the solution of the differential equation $dxdy +cos_{2}x3y =cos_{2}x1 $ and $y(4π )=34 $ then vaue of $y(−4π )$ is equal to (a) $−34 $ (b) $31 $ (c) $e_{6}+31 $ (d) $3$