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

The solution for y^{''}-4y=e^{3x} is y=c_{1}e^{2x}+c_{2}e^{-2x}+1/5 e^{3x}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 9 y^{^{'}} + 20 y = 3 x + e^{4 x}

y^{^{''}} - 4 y^{^{'}} + 3 = e^{- 5}, y (0) = 0, y^{^{'}} (0) = 0

x^{^{''}} - x^{^{'}} - 2 x = 5 cos (2 t)

y^{^{''}} - 14 y^{^{'}} + 49 y = 42 x + 4

y^{^{''}} + 4 y^{^{'}} + 6 y = 4 e^{(- 2 t)} cos (t)

What is the solution for y^{''}-4y=e^{3x} ?
The solution for y^{''}-4y=e^{3x} is y=c_{1}e^{2x}+c_{2}e^{-2x}+1/5 e^{3x}