What is the solution for y^{''}-12y^'+36y=7e^{6x} ?

The solution for y^{''}-12y^'+36y=7e^{6x} is y=c_{1}e^{6x}+c_{2}xe^{6x}+(7e^{6x}x^2)/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}-12y^'+36y=7e^{6x}

y^{^{''}} - 12 y^{^{'}} + 36 y = 7 e^{6 x}

y = c_{1} e^{6 x} + c_{2} x e^{6 x} + \frac{7 e ^{6 x} x ^{2}}{2}

Solution steps

y^{''} (x) - 12 y^{'} (x) + 36 y = 7 e^{6 x}

Solve linear ODE:

y = c_{1} e^{6 x} + c_{2} x e^{6 x} + \frac{7 e ^{6 x} x ^{2}}{2}

y = c_{1} e^{6 x} + c_{2} x e^{6 x} + \frac{7 e ^{6 x} x ^{2}}{2}

y^{^{''}} + \frac{1}{8} y^{^{'}} + y = 3 cos (t)

y^{^{''}} + 9 y^{^{'}} + 14 y = \frac{1}{2} sin (t)

(D^{2} - 4 D + 4) (y) = 6 x^{2} e^{2 x}

y^{^{'''}} - 6 y^{^{''}} + 12 y^{^{'}} - 8 y = t^{3} e^{2 t}

y^{^{''}} + y = sec^{2} (x), y (0) = 2, y^{^{'}} (0) = 1

What is the solution for y^{''}-12y^'+36y=7e^{6x} ?
The solution for y^{''}-12y^'+36y=7e^{6x} is y=c_{1}e^{6x}+c_{2}xe^{6x}+(7e^{6x}x^2)/2