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Popular >

y^{''}=-y

Solution

y^{^{''}} = - y

Solution

y = c_{1} cos (t) + c_{2} sin (t)

Solution steps

y^{''} (t) = - y

Solve linear ODE:

y = c_{1} cos (t) + c_{2} sin (t)

y = c_{1} cos (t) + c_{2} sin (t)

Popular Examples

y^{''}+7y^'=0,y(0)=8,y^'(0)=-3

y^{^{''}} + 7 y^{^{'}} = 0, y (0) = 8, y^{^{'}} (0) = - 3

y^{''}+4y^'+y32=0

y^{^{''}} + 4 y^{^{'}} + y 32 = 0

y^{''}-2y^'-3y=0,y^'(0)=4

y^{^{''}} - 2 y^{^{'}} - 3 y = 0, y^{^{'}} (0) = 4

36(d^2y)/(dx^2)+12(dy)/(dx)+y=0

36 \frac{d ^{2} y}{d x ^{2}} + 12 \frac{d y}{d x} + y = 0

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

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

Frequently Asked Questions (FAQ)

What is the solution for y^{''}=-y ?
The solution for y^{''}=-y is y=c_{1}cos(t)+c_{2}sin(t)