What is the solution for (d^2+1)y=x^2e^2x ?

The solution for (d^2+1)y=x^2e^2x is y=c_{1}cos(x)+c_{2}sin(x)+e^2x^3-6e^2x

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(d^2+1)y=x^2e^2x

(d^{2} + 1) y = x^{2} e^{2} x

y = c_{1} cos (x) + c_{2} sin (x) + e^{2} x^{3} - 6 e^{2} x

Solution steps

(d^{2} + 1) y = x^{2} e^{2} x

Solve linear ODE:

y = c_{1} cos (x) + c_{2} sin (x) + e^{2} x^{3} - 6 e^{2} x

y = c_{1} cos (x) + c_{2} sin (x) + e^{2} x^{3} - 6 e^{2} x

y^{^{''}} + y = \frac{1}{sin ( x )}

y^{^{''}} - 4 y^{^{'}} - 5 y = 4 x^{2} e^{2 x}

(d^{2} - 6 d + 9) \cdot y = x^{2} \cdot e^{2 x}

0.2 y^{^{''}} + 1.2 y^{^{'}} + 2 y = 5 cos (x)

(d^{2} + 4 d) y = 2 sin (3 x)

What is the solution for (d^2+1)y=x^2e^2x ?
The solution for (d^2+1)y=x^2e^2x is y=c_{1}cos(x)+c_{2}sin(x)+e^2x^3-6e^2x