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Popular >

y^{''}+2y^'-1=0

Solution

y^{^{''}} + 2 y^{^{'}} - 1 = 0

Solution

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

Solution steps

y^{''} (t) + 2 y^{'} (t) - 1 = 0

Solve linear ODE:

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

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

Popular Examples

y^{''}+4y^'+4y=x^2*e^{(-2x)}+1

y^{^{''}} + 4 y^{^{'}} + 4 y = x^{2} \cdot e^{(- 2 x)} + 1

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

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

y^{''}-y=sin(t),<y(0)=0,y^'(0)=1

y^{^{''}} - y = sin (t), < y (0) = 0, y^{^{'}} (0) = 1

5y^{''}+y^'=-2x,y(0)=0,y^'(0)=-20

5 y^{^{''}} + y^{^{'}} = - 2 x, y (0) = 0, y^{^{'}} (0) = - 20

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

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

Frequently Asked Questions (FAQ)

What is the solution for y^{''}+2y^'-1=0 ?
The solution for y^{''}+2y^'-1=0 is y=c_{1}+c_{2}e^{-2t}+t/2