What is the solution for y^{''}-y=2e^x-1-6*x*e^x ?

The solution for y^{''}-y=2e^x-1-6*x*e^x is y=c_{1}e^x+c_{2}e^{-x}+(-3e^xx^2+5e^xx)/2+1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}-y=2e^x-1-6xe^x

y^{^{''}} - y = 2 e^{x} - 1 - 6 \cdot x \cdot e^{x}

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

Solution steps

y^{''} (x) - y = 2 e^{x} - 1 - 6 \cdot x \cdot e^{x}

Solve linear ODE:

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

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

y^{^{'''}} + 4 y^{^{''}} - 5 y = x e^{x} + 17 x

x^{^{''}} - 4 x^{^{'}} + 4 x = 4 cos (2 t), x^{0} = 1, x^{^{'}} = - 1

y^{^{''}} + \frac{32}{3} y = cos (x)

y^{^{''}} + 4 y = t, y (0) = 0, y^{^{'}} (0) = 0

\frac{d ^{2} y}{d x ^{2}} - 16 y = x e^{x}

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