"Let y = y(x) be the solution of the differential equation xdy = (y + x3 cosx)dx with y($\pi$) = 0, then $y\left( {{\pi \over 2}} \right)$ is equal to :"

Question

Accepted Answer

"$xdy = (y + {x^3}\cos x)dx$

$\Rightarrow$ $xdy = ydx + {x^3}\cos xdx$

$\Rightarrow$ ${{xdy - ydx} \over {{x^2}}} = {{{x^3}coxdx} \over {{x^2}}}$

$\Rightarrow$ ${d \over {dx}}\left( {{y \over x}} \right) = \int {x\cos xdx}$

$\Rightarrow {y \over x} = x\sin x - \int {1.\sin xdx}$

$\Rightarrow$ ${y \over x} = x\sin x + \cos x + C$

$\Rightarrow 0 = - 1 + C \Rightarrow C = 1,x = \pi ,y = 0$

so, ${y \over x} = x\sin x + \cos x + 1$

$y = {x^2}\sin x + x\cos x + x$

$x = {\pi \over 2}$

$y\left( {{\pi \over 2}} \right) = {{{\pi ^2}} \over 4} + {\pi \over 2}$"

Let y = y(x) be the solution of the differential

equation xdy = (y + x³ cosx)dx with y($\pi$) = 0, then $y\left( {{\pi \over 2}} \right)$ is equal to :

Solution

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Let y = y(x) be the solution of the differential equation xdy = (y + x3 cosx)dx with y($\pi$) = 0, then $y\left( {{\pi \over 2}} \right)$ is equal to :

Solution

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More Differential Equations questions

Drill 25 more like these. Every day. Free.

Let y = y(x) be the solution of the differential

equation xdy = (y + x³ cosx)dx with y($\pi$) = 0, then $y\left( {{\pi \over 2}} \right)$ is equal to :