What is the solution for y^{''}+y=8xsin(x) ?

The solution for y^{''}+y=8xsin(x) is y=c_{1}cos(x)+c_{2}sin(x)-2x^2cos(x)+2xsin(x)

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y^{''}+y=8xsin(x)

y^{^{''}} + y = 8 x sin (x)

y = c_{1} cos (x) + c_{2} sin (x) - 2 x^{2} cos (x) + 2 x sin (x)

Solution steps

y^{''} (x) + y = 8 x sin (x)

Solve linear ODE:

y = c_{1} cos (x) + c_{2} sin (x) - 2 x^{2} cos (x) + 2 x sin (x)

y = c_{1} cos (x) + c_{2} sin (x) - 2 x^{2} cos (x) + 2 x sin (x)

\frac{\partial}{\partial x} (x^{2} - 2 x y + 4 y^{2})

x \to 6 lim (6 \cdot \frac{5}{6} \cdot (- \frac{2}{3}))

g (x) = x^{2} (1 - 9 x)

\int \frac{1}{3 - 2 y - y ^{2}} d y

\frac{\partial}{\partial y} (y cos (x y))

What is the solution for y^{''}+y=8xsin(x) ?
The solution for y^{''}+y=8xsin(x) is y=c_{1}cos(x)+c_{2}sin(x)-2x^2cos(x)+2xsin(x)