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Popular >

y^{''}-2y^'-8y=0,y(0)=a,y^'(0)=5

Solution

y^{^{''}} - 2 y^{^{'}} - 8 y = 0, y (0) = a, y^{^{'}} (0) = 5

Solution

y = e^{4 t} (a + \frac{5 - 4 a}{6}) - \frac{e ^{- 2 t} ( 5 - 4 a )}{6}

Solution steps

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

Solve linear ODE:

y = e^{4 t} (a + \frac{5 - 4 a}{6}) - \frac{e ^{- 2 t} ( 5 - 4 a )}{6}

y = e^{4 t} (a + \frac{5 - 4 a}{6}) - \frac{e ^{- 2 t} ( 5 - 4 a )}{6}

Graph

Popular Examples

x^{''}+4x^'+29x=0

x^{^{''}} + 4 x^{^{'}} + 29 x = 0

y^{'''}+2y^{''}-6y^'-72y=0,y(0)=e^{4x}

y^{^{'''}} + 2 y^{^{''}} - 6 y^{^{'}} - 72 y = 0, y (0) = e^{4 x}

y^{''}+6y^'+9y=0,y(-1)=2,y^'(-1)=2

y^{^{''}} + 6 y^{^{'}} + 9 y = 0, y (- 1) = 2, y^{^{'}} (- 1) = 2

y^{''''}+4y^{'''}-3y^{''}-y^'+1/2 y=0

y^{^{''''}} + 4 y^{^{'''}} - 3 y^{^{''}} - y^{^{'}} + \frac{1}{2} y = 0

y^{''}-6y^'+9y=0,y(0)=2,y^'(0)= 33/4

y^{^{''}} - 6 y^{^{'}} + 9 y = 0, y (0) = 2, y^{^{'}} (0) = \frac{33}{4}

Frequently Asked Questions (FAQ)

What is the solution for y^{''}-2y^'-8y=0,y(0)=a,y^'(0)=5 ?
The solution for y^{''}-2y^'-8y=0,y(0)=a,y^'(0)=5 is y=e^{4t}(a+(5-4a)/6)-(e^{-2t}(5-4a))/6