What is the solution for xy^'=y+x^2sin(x),y(pi/3)=0 ?

The solution for xy^'=y+x^2sin(x),y(pi/3)=0 is y=-xcos(x)+x/2

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xy^'=y+x^2sin(x),y(pi/3)=0

x y^{^{'}} = y + x^{2} sin (x), y (\frac{π}{3}) = 0

y = - x cos (x) + \frac{x}{2}

Solution steps

x y^{'} (x) = y + x^{2} sin (x)

Solve linear ODE:

y = - x cos (x) + \frac{x}{2}

y = - x cos (x) + \frac{x}{2}

h (31 - \frac{1}{2} h)^{2}

\int_{0}^{1} \frac{sin ( x )}{x} d x

\int 4 ln (4 x^{2}) d x

\frac{d}{d x} (\frac{a ^{2} + x ^{2}}{a ^{2} - x ^{2}})

What is the solution for xy^'=y+x^2sin(x),y(pi/3)=0 ?
The solution for xy^'=y+x^2sin(x),y(pi/3)=0 is y=-xcos(x)+x/2