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Popular >

y^{''}+13y^'+42y=7cos(4t)

Solution

y^{^{''}} + 13 y^{^{'}} + 42 y = 7 cos (4 t)

Solution

y = c_{1} e^{- 6 t} + c_{2} e^{- 7 t} + \frac{7}{65} sin (4 t) + \frac{7}{130} cos (4 t)

Solution steps

y^{''} (t) + 13 y^{'} (t) + 42 y = 7 cos (4 t)

Solve linear ODE:

y = c_{1} e^{- 6 t} + c_{2} e^{- 7 t} + \frac{7}{65} sin (4 t) + \frac{7}{130} cos (4 t)

y = c_{1} e^{- 6 t} + c_{2} e^{- 7 t} + \frac{7}{65} sin (4 t) + \frac{7}{130} cos (4 t)

Graph

Popular Examples

1/2 y^{''}+2y=2tan(2t)-1/2 e^{2t}

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

y^{'''}-4y^{''}+5y^'-2y=2e^{-x}+cos(x)

y^{^{'''}} - 4 y^{^{''}} + 5 y^{^{'}} - 2 y = 2 e^{- x} + cos (x)

y^{''''}+2y^{''}+2=0

y^{^{''''}} + 2 y^{^{''}} + 2 = 0

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

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

y^{''}+3y^'+2y=1,2e^ty(0)=2,y^'(0)=3

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

Frequently Asked Questions (FAQ)

What is the solution for y^{''}+13y^'+42y=7cos(4t) ?
The solution for y^{''}+13y^'+42y=7cos(4t) is y=c_{1}e^{-6t}+c_{2}e^{-7t}+7/65 sin(4t)+7/130 cos(4t)