What is the solution for y^{''}-2y^'+y=12e^{3t},y(0)=-1,y^'(0)=0 ?

The solution for y^{''}-2y^'+y=12e^{3t},y(0)=-1,y^'(0)=0 is y=-4e^t-5e^tt+3e^{3t}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}-2y^'+y=12e^{3t},y(0)=-1,y^'(0)=0

y^{^{''}} - 2 y^{^{'}} + y = 12 e^{3 t}, y (0) = - 1, y^{^{'}} (0) = 0

y = - 4 e^{t} - 5 e^{t} t + 3 e^{3 t}

Solution steps

y^{''} (t) - 2 y^{'} (t) + y = 12 e^{3 t}

Solve linear ODE:

y = - 4 e^{t} - 5 e^{t} t + 3 e^{3 t}

y = - 4 e^{t} - 5 e^{t} t + 3 e^{3 t}

2 y^{^{''}} - 4 y^{^{'}} + 2 y = e^{x} x^{- 1}

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} + 6 y = x^{2}

(D^{2} + 2 D + 1) y = e^{- 2 x} + 1

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

y^{^{''}} + 7 y^{^{'}} - 12 = e^{3 x} - 2 e^{x} - 5 x

What is the solution for y^{''}-2y^'+y=12e^{3t},y(0)=-1,y^'(0)=0 ?
The solution for y^{''}-2y^'+y=12e^{3t},y(0)=-1,y^'(0)=0 is y=-4e^t-5e^tt+3e^{3t}