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Popular >

x^{''}+81x=0

Solution

x^{^{''}} + 81 x = 0

Solution

x = c_{1} cos (9 t) + c_{2} sin (9 t)

Solution steps

x^{''} (t) + 81 x = 0

Solve linear ODE:

x = c_{1} cos (9 t) + c_{2} sin (9 t)

x = c_{1} cos (9 t) + c_{2} sin (9 t)

Popular Examples

(d^2y)/(dx^2)-10(dy)/(dx)+26y=0

\frac{d ^{2} y}{d x ^{2}} - 10 \frac{d y}{d x} + 26 y = 0

y^{^{'}} = 8 y^{^{''}}

y^{''}-4y^'+3y=0,y(0)=-1,y^'(0)=3

y^{^{''}} - 4 y^{^{'}} + 3 y = 0, y (0) = - 1, y^{^{'}} (0) = 3

y^{''}-6y^'+13y=0,y(0)=-3,y^'(0)=1

y^{^{''}} - 6 y^{^{'}} + 13 y = 0, y (0) = - 3, y^{^{'}} (0) = 1

y^{''}-5y^'+6y=0,y(0)=2,y^'(0)=5

y^{^{''}} - 5 y^{^{'}} + 6 y = 0, y (0) = 2, y^{^{'}} (0) = 5

Frequently Asked Questions (FAQ)

What is the solution for x^{''}+81x=0 ?
The solution for x^{''}+81x=0 is x=c_{1}cos(9t)+c_{2}sin(9t)