What is the solution for 2(d^2y)/(dx^2)+32y=0 ?

The solution for 2(d^2y)/(dx^2)+32y=0 is y=c_{1}cos(4x)+c_{2}sin(4x)

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2(d^2y)/(dx^2)+32y=0

2 \frac{d ^{2} y}{d x ^{2}} + 32 y = 0

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

Solution steps

2 \frac{d ^{2} y}{d x ^{2}} + 32 y = 0

Solve linear ODE:

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

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

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

\int \frac{6 x ^{3} - x ^{2} + 2 x - 1}{x ^{4} + x ^{2}} d x

\frac{d}{d x} (e^{2 x} + ln (2 x))

\int 3^{x} - 5 sin (2 x) d x

n = 0 \sum \infty (n + 1)^{2}

What is the solution for 2(d^2y)/(dx^2)+32y=0 ?
The solution for 2(d^2y)/(dx^2)+32y=0 is y=c_{1}cos(4x)+c_{2}sin(4x)