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Popular >

x^{''}-12x^'+36x=2t+e^{6t}

Solution

x^{^{''}} - 12 x^{^{'}} + 36 x = 2 t + e^{6 t}

Solution

x = c_{1} e^{6 t} + c_{2} t e^{6 t} + \frac{t}{18} + \frac{1}{54} + \frac{e ^{6 t} t ^{2}}{2}

Solution steps

x^{''} (t) - 12 x^{'} (t) + 36 x = 2 t + e^{6 t}

Solve linear ODE:

x = c_{1} e^{6 t} + c_{2} t e^{6 t} + \frac{t}{18} + \frac{1}{54} + \frac{e ^{6 t} t ^{2}}{2}

x = c_{1} e^{6 t} + c_{2} t e^{6 t} + \frac{t}{18} + \frac{1}{54} + \frac{e ^{6 t} t ^{2}}{2}

Graph

Popular Examples

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y^{^{''}} + 3 y^{^{'}} + 2 y = e^{2 x} cos (x)

Frequently Asked Questions (FAQ)

What is the solution for x^{''}-12x^'+36x=2t+e^{6t} ?
The solution for x^{''}-12x^'+36x=2t+e^{6t} is x=c_{1}e^{6t}+c_{2}te^{6t}+t/(18)+1/54+(e^{6t}t^2)/2