What is the solution for y^{''}-7y^'+10y=e^{3x}(-1+10x) ?

The solution for y^{''}-7y^'+10y=e^{3x}(-1+10x) is y=c_{1}e^{5x}+c_{2}e^{2x}-5xe^{3x}+3e^{3x}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

y^{''}-7y^'+10y=e^{3x}(-1+10x)

y^{^{''}} - 7 y^{^{'}} + 10 y = e^{3 x} (- 1 + 10 x)

y = c_{1} e^{5 x} + c_{2} e^{2 x} - 5 x e^{3 x} + 3 e^{3 x}

Solution steps

y^{''} (x) - 7 y^{'} (x) + 10 y = e^{3 x} (- 1 + 10 x)

Solve linear ODE:

y = c_{1} e^{5 x} + c_{2} e^{2 x} - 5 x e^{3 x} + 3 e^{3 x}

y = c_{1} e^{5 x} + c_{2} e^{2 x} - 5 x e^{3 x} + 3 e^{3 x}

What is the solution for y^{''}-7y^'+10y=e^{3x}(-1+10x) ?
The solution for y^{''}-7y^'+10y=e^{3x}(-1+10x) is y=c_{1}e^{5x}+c_{2}e^{2x}-5xe^{3x}+3e^{3x}