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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + 3 y^{^{'}} - 10 y = 3 x e^{- 2 x}

y^{^{''}} - 2 y^{^{''}} - 3 y = 9 x + 9

y^{^{'''}} - 9 y^{^{''}} + 27 y^{^{'}} - 27 y = 7 e^{3 x}

y^{^{''}} + 16 y = 50 e^{3} t, y (0) = 0, y^{^{'}} (0) = 0

4 y^{^{''}} - 8 y^{^{'}} + 5 y = e^{t} tan (\frac{t}{2})

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