What is the solution for y^{''}-12y^'+36y=5e^{2x} ?

The solution for y^{''}-12y^'+36y=5e^{2x} is y=c_{1}e^{6x}+c_{2}xe^{6x}+5/16 e^{2x}

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y^{''}-12y^'+36y=5e^{2x}

y^{^{''}} - 12 y^{^{'}} + 36 y = 5 e^{2 x}

y = c_{1} e^{6 x} + c_{2} x e^{6 x} + \frac{5}{16} e^{2 x}

Solution steps

y^{''} (x) - 12 y^{'} (x) + 36 y = 5 e^{2 x}

Solve linear ODE:

y = c_{1} e^{6 x} + c_{2} x e^{6 x} + \frac{5}{16} e^{2 x}

y = c_{1} e^{6 x} + c_{2} x e^{6 x} + \frac{5}{16} e^{2 x}

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

x^{^{''}} + 2 x^{^{'}} + x = e^{2 t}, x (0) = 2, x^{^{'}} (0) = 1

4 y^{^{''}} - 4 y^{^{'}} - 3 y = 0

4 y^{^{''}} - 4 y^{^{'}} + y = 0

\frac{d ^{2} y}{d x ^{2}} + 5 \frac{d y}{d x} + 10 y = 0

What is the solution for y^{''}-12y^'+36y=5e^{2x} ?
The solution for y^{''}-12y^'+36y=5e^{2x} is y=c_{1}e^{6x}+c_{2}xe^{6x}+5/16 e^{2x}