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Popular >

y^{''}+y^'=c

Solution

y^{^{''}} + y^{^{'}} = c

Solution

y = c_{1} + c_{2} e^{- t} + c t

Solution steps

y^{''} (t) + y^{'} (t) = c

Solve linear ODE:

y = c_{1} + c_{2} e^{- t} + c t

y = c_{1} + c_{2} e^{- t} + c t

Graph

Popular Examples

(D^3-5D^2+8D-4)y=e^{2x}+2e^x+3e^{-x}

(D^{3} - 5 D^{2} + 8 D - 4) y = e^{2 x} + 2 e^{x} + 3 e^{- x}

y^{''}-16y=16t-32e^{-4t},y(0)=0,y^'(0)=51

y^{^{''}} - 16 y = 16 t - 32 e^{- 4 t}, y (0) = 0, y^{^{'}} (0) = 51

y^{''}+2y^'+1000y=2e^{2x}

y^{^{''}} + 2 y^{^{'}} + 1000 y = 2 e^{2 x}

y^{''}+2y^'+10y=2cos(x)

y^{^{''}} + 2 y^{^{'}} + 10 y = 2 cos (x)

2x^{''}+5x^'+2x=4e-2t-t

2 x^{^{''}} + 5 x^{^{'}} + 2 x = 4 e - 2 t - t

Frequently Asked Questions (FAQ)

What is the solution for y^{''}+y^'=c ?
The solution for y^{''}+y^'=c is y=c_{1}+c_{2}e^{-t}+ct