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Popular >

y^{''}= y/4

Solution

y^{^{''}} = \frac{y}{4}

Solution

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

Solution steps

y^{''} (t) = \frac{y}{4}

Solve linear ODE:

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

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

Popular Examples

y^{''}-4y^'+8y=0,y^'(0)=2,y(0)=0

y^{^{''}} - 4 y^{^{'}} + 8 y = 0, y^{^{'}} (0) = 2, y (0) = 0

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

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

y^{''}+4y^1-y=0

y^{^{''}} + 4 y^{1} - y = 0

y^{''}+pi^2*y=0

y^{^{''}} + π^{2} \cdot y = 0

y^{''}+16y^'+100y=0,y(0)=0,y^'(0)=0

y^{^{''}} + 16 y^{^{'}} + 100 y = 0, y (0) = 0, y^{^{'}} (0) = 0

Frequently Asked Questions (FAQ)

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