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Popular >

y^{''}+3y^'=4

Solution

y^{^{''}} + 3 y^{^{'}} = 4

Solution

y = c_{1} + c_{2} e^{- 3 t} + \frac{4 t}{3}

Solution steps

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

Solve linear ODE:

y = c_{1} + c_{2} e^{- 3 t} + \frac{4 t}{3}

y = c_{1} + c_{2} e^{- 3 t} + \frac{4 t}{3}

Popular Examples

2y^{''}+y^'-y=3x+4,y(0)=1,y^'(0)=1

2 y^{^{''}} + y^{^{'}} - y = 3 x + 4, y (0) = 1, y^{^{'}} (0) = 1

y^{''}+9y=18sin(3t)

y^{^{''}} + 9 y = 18 sin (3 t)

y^{''}-y^'-6y=3e^{2x}

y^{^{''}} - y^{^{'}} - 6 y = 3 e^{2 x}

x^{''}+25x=cos(t)

x^{^{''}} + 25 x = cos (t)

y^{''}+7y^'-12y=e^3x-2e^x-5x

y^{^{''}} + 7 y^{^{'}} - 12 y = e^{3} x - 2 e^{x} - 5 x

Frequently Asked Questions (FAQ)

What is the solution for y^{''}+3y^'=4 ?
The solution for y^{''}+3y^'=4 is y=c_{1}+c_{2}e^{-3t}+(4t)/3