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Popular Calculus >

y^{''}+2y^'+5y=3\H(t)

Solution

y^{^{''}} + 2 y^{^{'}} + 5 y = 3 H (t)

Solution

y = e^{- t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + e^{- t} cos (2 t) \cdot \int - \frac{3 e ^{t} sin ( 2 t ) H ( t )}{2} d t + e^{- t} sin (2 t) \cdot \int \frac{3 e ^{t} cos ( 2 t ) H ( t )}{2} d t

Solution steps

y^{''} (t) + 2 y^{'} (t) + 5 y = 3 H (t)

Solve linear ODE:

y = e^{- t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + e^{- t} cos (2 t) \cdot \int - \frac{3 e ^{t} sin ( 2 t ) H ( t )}{2} d t + e^{- t} sin (2 t) \cdot \int \frac{3 e ^{t} cos ( 2 t ) H ( t )}{2} d t

y = e^{- t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + e^{- t} cos (2 t) \cdot \int - \frac{3 e ^{t} sin ( 2 t ) H ( t )}{2} d t + e^{- t} sin (2 t) \cdot \int \frac{3 e ^{t} cos ( 2 t ) H ( t )}{2} d t

Popular Examples

y^{''}-2y^'=3,y(0)=-3e^{-x}

y^{''}+9y^'+18y=x+e^{-x}

(D^2+1)y=sec(xtan(x))

4x^{''}+kx=8sin(t)

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

Frequently Asked Questions (FAQ)

What is the solution for y^{''}+2y^'+5y=3\H(t) ?
The solution for y^{''}+2y^'+5y=3\H(t) is