What is the solution for y^{''}-5y^'+6y=2x+3e^{2x} ?

The solution for y^{''}-5y^'+6y=2x+3e^{2x} is y=c_{1}e^{3x}+c_{2}e^{2x}+x/3+5/18-3xe^{2x}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}-5y^'+6y=2x+3e^{2x}

y^{^{''}} - 5 y^{^{'}} + 6 y = 2 x + 3 e^{2 x}

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x}{3} + \frac{5}{18} - 3 x e^{2 x}

Solution steps

y^{''} (x) - 5 y^{'} (x) + 6 y = 2 x + 3 e^{2 x}

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x}{3} + \frac{5}{18} - 3 x e^{2 x}

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x}{3} + \frac{5}{18} - 3 x e^{2 x}

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} - 3 y = 3 x e^{2 x}

y^{^{''}} - 2 y^{^{'}} + y = 3 x^{2} + 6 + 4 e x

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

y^{^{''}} + 9 y = 12 cos (3 x)

2 y^{^{''}} + 3 y^{^{'}} + y = x^{2}

What is the solution for y^{''}-5y^'+6y=2x+3e^{2x} ?
The solution for y^{''}-5y^'+6y=2x+3e^{2x} is y=c_{1}e^{3x}+c_{2}e^{2x}+x/3+5/18-3xe^{2x}