What is the solution for x^{''}-14x^'+49x=5te^{7t} ?

The solution for x^{''}-14x^'+49x=5te^{7t} is x=c_{1}e^{7t}+c_{2}te^{7t}+(5e^{7t}t^3)/6

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

x^{''}-14x^'+49x=5te^{7t}

x^{^{''}} - 14 x^{^{'}} + 49 x = 5 t e^{7 t}

x = c_{1} e^{7 t} + c_{2} t e^{7 t} + \frac{5 e ^{7 t} t ^{3}}{6}

Solution steps

x^{''} (t) - 14 x^{'} (t) + 49 x = 5 t e^{7 t}

Solve linear ODE:

x = c_{1} e^{7 t} + c_{2} t e^{7 t} + \frac{5 e ^{7 t} t ^{3}}{6}

x = c_{1} e^{7 t} + c_{2} t e^{7 t} + \frac{5 e ^{7 t} t ^{3}}{6}

What is the solution for x^{''}-14x^'+49x=5te^{7t} ?
The solution for x^{''}-14x^'+49x=5te^{7t} is x=c_{1}e^{7t}+c_{2}te^{7t}+(5e^{7t}t^3)/6