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Popular >

y^{''}+2y^'+y=0,y(1)=8,y^'(0)=6

Solution

y^{^{''}} + 2 y^{^{'}} + y = 0, y (1) = 8, y^{^{'}} (0) = 6

Solution

y = (8 e - \frac{6 + 8 e}{2}) e^{- t} + \frac{( 6 + 8 e ) e ^{- t} t}{2}

Solution steps

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

Solve linear ODE:

y = (8 e - \frac{6 + 8 e}{2}) e^{- t} + \frac{( 6 + 8 e ) e ^{- t} t}{2}

y = (8 e - \frac{6 + 8 e}{2}) e^{- t} + \frac{( 6 + 8 e ) e ^{- t} t}{2}

Popular Examples

36y^{''}+132y^'+121y=0,y(0)=5,y^'(0)=5

36 y^{^{''}} + 132 y^{^{'}} + 121 y = 0, y (0) = 5, y^{^{'}} (0) = 5

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

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

y^{''}+2y^'+2y=0,y(pi/4)=0,y^'(pi/4)=-2

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

linear y^{'''}+19y^{''}-14y^'-266y=0 linear

y^{^{'''}} + 19 y^{^{''}} - 14 y^{^{'}} - 266 y = 0

40y^{''}-ay^'+4000y=0

40 y^{^{''}} - a y^{^{'}} + 4000 y = 0

Frequently Asked Questions (FAQ)

What is the solution for y^{''}+2y^'+y=0,y(1)=8,y^'(0)=6 ?
The solution for y^{''}+2y^'+y=0,y(1)=8,y^'(0)=6 is y=(8e-(6+8e)/2)e^{-t}+((6+8e)e^{-t}t)/2