What is the solution for (d^2y)/(dx^2)=-25y ?

The solution for (d^2y)/(dx^2)=-25y is y=c_{1}cos(5x)+c_{2}sin(5x)

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(d^2y)/(dx^2)=-25y

\frac{d ^{2} y}{d x ^{2}} = - 25 y

y = c_{1} cos (5 x) + c_{2} sin (5 x)

Solution steps

\frac{d ^{2} y}{d x ^{2}} = - 25 y

Solve linear ODE:

y = c_{1} cos (5 x) + c_{2} sin (5 x)

y = c_{1} cos (5 x) + c_{2} sin (5 x)

\frac{e ^{2 t} - e ^{1}}{2}

\int_{0}^{1} π (x)^{2} d x

h \to 0 lim (3 h - 1)

x^{3} + y^{2} x^{4} + 2 y^{^{'}} = 0

\int \frac{1}{4 x} d x

What is the solution for (d^2y)/(dx^2)=-25y ?
The solution for (d^2y)/(dx^2)=-25y is y=c_{1}cos(5x)+c_{2}sin(5x)