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Popular >

y^{''}+3y^'=7

Solution

y^{^{''}} + 3 y^{^{'}} = 7

Solution

y = c_{1} + c_{2} e^{- 3 t} + \frac{7 t}{3}

Solution steps

y^{''} (t) + 3 y^{'} (t) = 7

Solve linear ODE:

y = c_{1} + c_{2} e^{- 3 t} + \frac{7 t}{3}

y = c_{1} + c_{2} e^{- 3 t} + \frac{7 t}{3}

Popular Examples

y^{''}-6y^'+25y=64e^{-x}

y^{^{''}} - 6 y^{^{'}} + 25 y = 64 e^{- x}

y^{''}+9y=5e^x-162x^2

y^{^{''}} + 9 y = 5 e^{x} - 162 x^{2}

y^{''}+3y^'+2y=(1+e^x)^{-1}

y^{^{''}} + 3 y^{^{'}} + 2 y = (1 + e^{x})^{- 1}

y^{''}-4y^'+4y=x^3e^{2x}+xe^{-2x}

y^{^{''}} - 4 y^{^{'}} + 4 y = x^{3} e^{2 x} + x e^{- 2 x}

y^{''}+2y^'+2y=\H(t-pi)

y^{^{''}} + 2 y^{^{'}} + 2 y = H (t - π)

Frequently Asked Questions (FAQ)

What is the solution for y^{''}+3y^'=7 ?
The solution for y^{''}+3y^'=7 is y=c_{1}+c_{2}e^{-3t}+(7t)/3