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Popular >

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

Solution

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

Solution

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

Solution steps

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

Solve linear ODE:

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

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

Graph

Popular Examples

y^{''''}+8y^{'''}+24y^{''}+32y^'+16y=0

y^{^{''''}} + 8 y^{^{'''}} + 24 y^{^{''}} + 32 y^{^{'}} + 16 y = 0

linear (d^2y)/(dx^2)+5(dy)/(dx)+10y=0 linear

\frac{d ^{2} y}{d x ^{2}} + 5 \frac{d y}{d x} + 10 y = 0

θ^{''}(t)+(4k)/3 θ(t)=0

θ^{^{''}} (t) + \frac{4 k}{3} θ (t) = 0

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

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

y^{''}+4y^'-12y=0,y(0)=7,y^'(0)=-7

y^{^{''}} + 4 y^{^{'}} - 12 y = 0, y (0) = 7, y^{^{'}} (0) = - 7

Frequently Asked Questions (FAQ)

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