Solving a differential equation with trigonometric functions How could I approach y−A⋅sin⁡(d2ydx2)=0

Gabriela Duarte

Gabriela Duarte

Answered

2022-01-27

Solving a differential equation with trigonometric functions
How could I approach
yAsin(d2ydx2)=0

Answer & Explanation

helsinka04

helsinka04

Expert

2022-01-28Added 11 answers

Hint:
Let s=y′.
Then,
y=Asindsdx=Asindsdydydx=Asinsdsdy
Rearranging yields
sds=dysin1yA
You should finally obtain
2x+C2=dy(ysin1yA+A1y2A2+C1)12
The integral can be rewritten into
AcosgC1+A(gsing+cosg)dg
by letting y=Asing
I do not expect the integral is elementary

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