What is the solution for (d^2+4)y=e^3x ?

The solution for (d^2+4)y=e^3x is y=c_{1}cos(2x)+c_{2}sin(2x)+(e^3x)/4

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(d^2+4)y=e^3x

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

y = c_{1} cos (2 x) + c_{2} sin (2 x) + \frac{e ^{3} x}{4}

Solution steps

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

Solve linear ODE:

y = c_{1} cos (2 x) + c_{2} sin (2 x) + \frac{e ^{3} x}{4}

y = c_{1} cos (2 x) + c_{2} sin (2 x) + \frac{e ^{3} x}{4}

(d - 1)^{2} \cdot y = sin (x) \cdot x^{2} \cdot e^{x}

(d^{3} + 1) \cdot y = cos (2 x - 1)

y^{^{''}} + y^{^{'}} + y = x^{2} + 3 x

(d^{2} + 9) y = sin^{3} (x)

(d^{2} + 2) y = e^{x} \cdot cos^{3} (x)

What is the solution for (d^2+4)y=e^3x ?
The solution for (d^2+4)y=e^3x is y=c_{1}cos(2x)+c_{2}sin(2x)+(e^3x)/4