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

The solution for y^{''}-2y^'-3y=6xe^{3x} is y=c_{1}e^{3x}+c_{2}e^{-x}+(3e^{3x}x^2)/4-(3e^{3x}x)/8

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}-2y^'-3y=6xe^{3x}

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

y = c_{1} e^{3 x} + c_{2} e^{- x} + \frac{3 e ^{3 x} x ^{2}}{4} - \frac{3 e ^{3 x} x}{8}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- x} + \frac{3 e ^{3 x} x ^{2}}{4} - \frac{3 e ^{3 x} x}{8}

y = c_{1} e^{3 x} + c_{2} e^{- x} + \frac{3 e ^{3 x} x ^{2}}{4} - \frac{3 e ^{3 x} x}{8}

y^{^{''}} + 4 y^{^{'}} + 3 y = e^{5 x}

y^{^{'''}} - 6 y^{^{''}} + 11 y^{^{'}} - 6 y + x^{2} = - 1

x^{^{''}} + 5 x^{^{'}} + 4 x = 12.5 cos (4 t)

x^{^{''}} - 4 x^{^{'}} + 4 x = 4 e^{2 t}

y^{^{''}} - 4 y = 2 e^{4 t}

What is the solution for y^{''}-2y^'-3y=6xe^{3x} ?
The solution for y^{''}-2y^'-3y=6xe^{3x} is y=c_{1}e^{3x}+c_{2}e^{-x}+(3e^{3x}x^2)/4-(3e^{3x}x)/8