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Popular >

y^{''}+4^2y=0

Solution

y^{^{''}} + 4^{2} y = 0

Solution

y = c_{1} cos (4 t) + c_{2} sin (4 t)

Solution steps

y^{''} (t) + 4^{2} y = 0

Solve linear ODE:

y = c_{1} cos (4 t) + c_{2} sin (4 t)

y = c_{1} cos (4 t) + c_{2} sin (4 t)

Graph

Popular Examples

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

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

y^{''}-y^'+4y=0

y^{^{''}} - y^{^{'}} + 4 y = 0

y^{'''}-13y^{''}+50y^'-56y=0

y^{^{'''}} - 13 y^{^{''}} + 50 y^{^{'}} - 56 y = 0

(d^2f)/(dx^2)=f(x),f^'(pi)=0,f^'(0)=0

\frac{d ^{2} f}{d x ^{2}} = f (x), f^{^{'}} (π) = 0, f^{^{'}} (0) = 0

y^{''}-12y^'+32y=0,y(0)=-1,y^'(0)=-2

y^{^{''}} - 12 y^{^{'}} + 32 y = 0, y (0) = - 1, y^{^{'}} (0) = - 2

Frequently Asked Questions (FAQ)

What is the solution for y^{''}+4^2y=0 ?
The solution for y^{''}+4^2y=0 is y=c_{1}cos(4t)+c_{2}sin(4t)