What is the solution for y^{''}+y-7xsin(x)=0 ?

The solution for y^{''}+y-7xsin(x)=0 is y=c_{1}cos(x)+c_{2}sin(x)-(7x^2cos(x))/4+(7xsin(x))/4

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y^{''}+y-7xsin(x)=0

y^{^{''}} + y - 7 x sin (x) = 0

y = c_{1} cos (x) + c_{2} sin (x) - \frac{7 x ^{2} cos ( x )}{4} + \frac{7 x sin ( x )}{4}

Solution steps

y^{''} (x) + y - 7 x sin (x) = 0

Solve linear ODE:

y = c_{1} cos (x) + c_{2} sin (x) - \frac{7 x ^{2} cos ( x )}{4} + \frac{7 x sin ( x )}{4}

y = c_{1} cos (x) + c_{2} sin (x) - \frac{7 x ^{2} cos ( x )}{4} + \frac{7 x sin ( x )}{4}

What is the solution for y^{''}+y-7xsin(x)=0 ?
The solution for y^{''}+y-7xsin(x)=0 is y=c_{1}cos(x)+c_{2}sin(x)-(7x^2cos(x))/4+(7xsin(x))/4