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Popular Calculus >

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

Solution

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

Solution

y = e^{\frac{5 t}{2}} (c_{1} cos (\frac{3 t}{2}) + c_{2} sin (\frac{3 t}{2})) + e^{- \frac{5 t}{2}} (c_{3} cos (\frac{3 t}{2}) + c_{4} sin (\frac{3 t}{2}))

Solution steps

y^{(4)} (t) - y^{''} (t) + 4 y = 0

Solve linear ODE:

y = e^{\frac{5 t}{2}} (c_{1} cos (\frac{3 t}{2}) + c_{2} sin (\frac{3 t}{2})) + e^{- \frac{5 t}{2}} (c_{3} cos (\frac{3 t}{2}) + c_{4} sin (\frac{3 t}{2}))

y = e^{\frac{5 t}{2}} (c_{1} cos (\frac{3 t}{2}) + c_{2} sin (\frac{3 t}{2})) + e^{- \frac{5 t}{2}} (c_{3} cos (\frac{3 t}{2}) + c_{4} sin (\frac{3 t}{2}))

Graph

Popular Examples

6y^{''}+17y^'-3y=0

y^{''}-15y^'+56y=0

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

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

y^{'''}-5y^{''}+7y^'-3y=0

Frequently Asked Questions (FAQ)

What is the solution for y^{''''}-y^{''}+4y=0 ?
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