en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

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

Solution

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

Solution steps

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

Solve linear ODE:

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

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

Popular Examples

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

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

(d^2y)/(dx^2)-3(dy)/(dx)=2e^{2x}sin(x)

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

y^{''}+6y^'+13y=10e^{-2t}

y^{^{''}} + 6 y^{^{'}} + 13 y = 10 e^{- 2 t}

y^{''}+y=t+tsin(t)

y^{^{''}} + y = t + t sin (t)

y^{''}+11y^'+18y=5sin(3x)

y^{^{''}} + 11 y^{^{'}} + 18 y = 5 sin (3 x)

Frequently Asked Questions (FAQ)

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