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Popular >

x^{''}+a^2x=0

Solution

x^{^{''}} + a^{2} x = 0

Solution

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

Solution steps

x^{''} (t) + a^{2} x = 0

Solve linear ODE:

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

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

Graph

Popular Examples

y^{''}-14y^'+40y=0

y^{^{''}} - 14 y^{^{'}} + 40 y = 0

y^{''}-2y^'+10y=0,y(0)=4,y^'(0)=5

y^{^{''}} - 2 y^{^{'}} + 10 y = 0, y (0) = 4, y^{^{'}} (0) = 5

(d^2y)/(dx^2)-2(dy)/(dx)+5y=0

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} + 5 y = 0

1/(pi^2)x^{''}+16x=0

\frac{1}{π ^{2}} x^{^{''}} + 16 x = 0

6y^{''}-7y^'-3y=0

6 y^{^{''}} - 7 y^{^{'}} - 3 y = 0

Frequently Asked Questions (FAQ)

What is the solution for x^{''}+a^2x=0 ?
The solution for x^{''}+a^2x=0 is x=c_{1}cos(at)+c_{2}sin(at)