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Popular >

y^{''}-2y^'-8y=0,y(0)=a,y^'(0)=-8

Solution

y^{^{''}} - 2 y^{^{'}} - 8 y = 0, y (0) = a, y^{^{'}} (0) = - 8

Solution

y = e^{4 t} (a - \frac{2 ( a + 2 )}{3}) + \frac{2 e ^{- 2 t} ( a + 2 )}{3}

Solution steps

y^{''} (t) - 2 y^{'} (t) - 8 y = 0

Solve linear ODE:

y = e^{4 t} (a - \frac{2 ( a + 2 )}{3}) + \frac{2 e ^{- 2 t} ( a + 2 )}{3}

y = e^{4 t} (a - \frac{2 ( a + 2 )}{3}) + \frac{2 e ^{- 2 t} ( a + 2 )}{3}

Graph

Popular Examples

y^{''}+7y^'=0,y(0)=-1,y^'(0)=-1

y^{^{''}} + 7 y^{^{'}} = 0, y (0) = - 1, y^{^{'}} (0) = - 1

y^{''}+3y^'=0,y^'(0)=0,y(0)=0

y^{^{''}} + 3 y^{^{'}} = 0, y^{^{'}} (0) = 0, y (0) = 0

y^{''}+6y^'+9y=0,y(-1)=5,y^'(-1)=5

y^{^{''}} + 6 y^{^{'}} + 9 y = 0, y (- 1) = 5, y^{^{'}} (- 1) = 5

2y^{''}+12y^'+24y=0,y(0)=1,y^'(0)=4

2 y^{^{''}} + 12 y^{^{'}} + 24 y = 0, y (0) = 1, y^{^{'}} (0) = 4

5y^{''}-y^'-8y=0

5 y^{^{''}} - y^{^{'}} - 8 y = 0

Frequently Asked Questions (FAQ)

What is the solution for y^{''}-2y^'-8y=0,y(0)=a,y^'(0)=-8 ?
The solution for y^{''}-2y^'-8y=0,y(0)=a,y^'(0)=-8 is y=e^{4t}(a-(2(a+2))/3)+(2e^{-2t}(a+2))/3