What is the solution for y^{''}+y^'=3e^{x/2} ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

y^{^{''}} + y^{^{'}} = 3 e^{\frac{x}{2}}

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

Solution steps

y^{''} (x) + y^{'} (x) = 3 e^{\frac{x}{2}}

Solve linear ODE:

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

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

y^{^{''}} - 2 y^{^{'}} - 3 y = 3 e^{5 t}

y^{^{''}} + 36 y = 8 cos (6 x) + 12 sin (6 x)

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} - 5 y = 24 e^{x}

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 3 y = 6 x^{2} + 19 x + 5

y^{^{'''}} + y^{^{''}} - 2 y = x e^{x} + 5

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