What is the solution for y^{''}-7y^'+12y=6e^t ?

The solution for y^{''}-7y^'+12y=6e^t is y=c_{1}e^{4t}+c_{2}e^{3t}+e^t

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}-7y^'+12y=6e^t

y^{^{''}} - 7 y^{^{'}} + 12 y = 6 e^{t}

y = c_{1} e^{4 t} + c_{2} e^{3 t} + e^{t}

Solution steps

y^{''} (t) - 7 y^{'} (t) + 12 y = 6 e^{t}

Solve linear ODE:

y = c_{1} e^{4 t} + c_{2} e^{3 t} + e^{t}

y = c_{1} e^{4 t} + c_{2} e^{3 t} + e^{t}

\frac{d}{d t} (x (t, y)), y = 4 x (t, y)

\frac{d}{d x} (\frac{1}{1 - x ^{3}})

x \to 7 lim (9)

\int \frac{1}{( 1 + t ^{2} )} d t

\frac{d}{d x} (e^{x} (cos (x) + sin (x)))

What is the solution for y^{''}-7y^'+12y=6e^t ?
The solution for y^{''}-7y^'+12y=6e^t is y=c_{1}e^{4t}+c_{2}e^{3t}+e^t