What is the solution for y^{''}-4y^'=3xe^x+2 ?

The solution for y^{''}-4y^'=3xe^x+2 is y=c_{1}e^{4x}+c_{2}-e^xx+2/3 e^x-x/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

y = c_{1} e^{4 x} + c_{2} - e^{x} x + \frac{2}{3} e^{x} - \frac{x}{2}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} - e^{x} x + \frac{2}{3} e^{x} - \frac{x}{2}

y = c_{1} e^{4 x} + c_{2} - e^{x} x + \frac{2}{3} e^{x} - \frac{x}{2}

y^{^{''}} + 25 y = 8 cos (5 x) + 12 sin (5 x)

y^{^{''}} - 6 y^{^{'}} + 25 y = 2 sin (\frac{x}{2}) - cos (\frac{x}{2})

y^{^{''}} + 4 y^{^{'}} + 5 y = e^{- 2 x} sin (x)

y^{^{''}} + 8 y^{^{'}} + 20 y = 100 x^{2} - 26 x e^{x}

y^{^{''}} + 9 y = 3 csc^{2} (3 x)

What is the solution for y^{''}-4y^'=3xe^x+2 ?
The solution for y^{''}-4y^'=3xe^x+2 is y=c_{1}e^{4x}+c_{2}-e^xx+2/3 e^x-x/2