What is the solution for q^{''}+100q^'+2500q=40,q(0)=0 ?

The solution for q^{''}+100q^'+2500q=40,q(0)=0 is q(t)=-2/125 e^{-50t}+c_{2}e^{-50t}t+2/125

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

q^{''}+100q^'+2500q=40,q(0)=0

q^{^{''}} + 100 q^{^{'}} + 2500 q = 40, q (0) = 0

q (t) = - \frac{2}{125} e^{- 50 t} + c_{2} e^{- 50 t} t + \frac{2}{125}

Solution steps

q^{''} (t) + 100 q^{'} (t) + 2500 q (t) = 40

Solve linear ODE:

q (t) = - \frac{2}{125} e^{- 50 t} + c_{2} e^{- 50 t} t + \frac{2}{125}

q (t) = - \frac{2}{125} e^{- 50 t} + c_{2} e^{- 50 t} t + \frac{2}{125}

(D^{2} + 5) y = cos (5) x

(D^{2} + 4 D + 4) y = 5 e^{3 x}

3 y^{^{'}} + 2 y^{^{''}} = - 1000 cos (3.14 \cdot \frac{t}{0.2})

y^{^{''}} - \frac{1}{2} y^{^{'}} - 1 = 0, y (0) = 100, y (3) = 10

\frac{1}{2} y^{^{''}} + 2 y = 3 tan (2 t) - \frac{1}{2} e^{2 t}

What is the solution for q^{''}+100q^'+2500q=40,q(0)=0 ?
The solution for q^{''}+100q^'+2500q=40,q(0)=0 is q(t)=-2/125 e^{-50t}+c_{2}e^{-50t}t+2/125