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Popular >

y^{''}+r^2y=0

Solution

y^{^{''}} + r^{2} y = 0

Solution

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

Solution steps

y^{''} (t) + r^{2} y = 0

Solve linear ODE:

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

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

Graph

Popular Examples

t''+4t(x(t,z))=0,t(0)=-5,t^'(0)=2

t^{''} + 4 t (x (t, z)) = 0, t (0) = - 5, t^{^{'}} (0) = 2

x^{''}+2x^'+26x=0,x(0)=1,x^'(0)=4

x^{^{''}} + 2 x^{^{'}} + 26 x = 0, x (0) = 1, x^{^{'}} (0) = 4

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

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

(d^2y)/(dx^2)=-k^2y

\frac{d ^{2} y}{d x ^{2}} = - k^{2} y

x^{''}+144x=0,x(0)=3,x^'(0)=-48

x^{^{''}} + 144 x = 0, x (0) = 3, x^{^{'}} (0) = - 48

Frequently Asked Questions (FAQ)

What is the solution for y^{''}+r^2y=0 ?
The solution for y^{''}+r^2y=0 is y=c_{1}cos(rt)+c_{2}sin(rt)