What is the solution for 4y^{''}-y=e^{x/2}+8 ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

4y^{''}-y=e^{x/2}+8

4 y^{^{''}} - y = e^{\frac{x}{2}} + 8

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

Solution steps

4 y^{''} (x) - y = e^{\frac{x}{2}} + 8

Solve linear ODE:

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

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

y^{^{''}} - 3 y^{^{'}} - 4 y = 5 e^{- x}, y (0) = 1, y^{^{'}} (0) = 13

y^{^{''}} - 4 y^{^{'}} + 4 y = e^{2 x} - 6

y^{^{''}} - y^{^{'}} - 2 y = 1 + t, y (0) = 2, y^{^{'}} (0) = 0

\frac{5}{3} y^{^{''}} + 10 y^{^{'}} + 30 y = 300

3 y^{^{''}} - 4 y^{^{'}} + y = x - 7

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