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Popular >

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

Solution

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

Solution

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

Solution steps

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

Solve linear ODE:

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

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

Graph

Popular Examples

y^{''}+4y^'+40y=0,y(0)=0,y^'(0)=0

y^{^{''}} + 4 y^{^{'}} + 40 y = 0, y (0) = 0, y^{^{'}} (0) = 0

x^{^{''}} - 0.5 x = 0

y^{''}+36y=0,y(0)=-5,y^'(0)=12

y^{^{''}} + 36 y = 0, y (0) = - 5, y^{^{'}} (0) = 12

y^{'''''}-16y^'=0

y^{^{'''''}} - 16 y^{^{'}} = 0

0.2y^{''}+5y^'+500y=0,y(0)=1,y^'(0)=0

0.2 y^{^{''}} + 5 y^{^{'}} + 500 y = 0, y (0) = 1, y^{^{'}} (0) = 0

Frequently Asked Questions (FAQ)

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