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Popular >

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

Solution

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

Solution

y = e^{- t} (c_{1} cos (t) + c_{2} sin (t)) + \frac{e ^{- t} t sin ( t )}{2}

Solution steps

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

Solve linear ODE:

y = e^{- t} (c_{1} cos (t) + c_{2} sin (t)) + \frac{e ^{- t} t sin ( t )}{2}

y = e^{- t} (c_{1} cos (t) + c_{2} sin (t)) + \frac{e ^{- t} t sin ( t )}{2}

Popular Examples

derivative of ln(e^{sin(x}*x^{cos(x)}))

\frac{d}{d x} (ln (e^{s i n (x)} \cdot x^{c o s (x)}))

limit as x approaches-1 of x^3+3x^2-2x-3

x \to - 1 lim (x^{3} + 3 x^{2} - 2 x - 3)

ty^'+4y=t^3,y(2)=4

t y^{^{'}} + 4 y = t^{3}, y (2) = 4

derivative of w/(sqrt(1-4x^2))

\frac{d}{d x} (\frac{w}{1 - 4 x ^{2}})

derivative of 2t^{-1/4}+2ln(t)+ln(5)derivative of

2 t^{- \frac{1}{4}} + 2 ln (t) + ln (5)

Frequently Asked Questions (FAQ)

What is the solution for y^{''}+2y^'+2y=e^{-t}cos(t) ?
The solution for y^{''}+2y^'+2y=e^{-t}cos(t) is y=e^{-t}(c_{1}cos(t)+c_{2}sin(t))+(e^{-t}tsin(t))/2