Question

Solusi dari persamaan sin xdx + ydy = 0; y(0)=-2

Answer 1

Let us solve the equation $\sin xdx + ydy = 0; y(0)=-2$:

$\sin xdx =- ydy$

$\int \sin xdx = -\int ydy$

$-\cos x=-\frac{y^2}{2}+C$

Since $y(0)=-2$, we have the equation $-\cos 0=-\frac{(-2)^2}{2}+C$ which is equivalent to $-1=-2+C$. So, $C=1.$

Therefore,

$-\cos x=-\frac{y^2}{2}+1$ or

$y^2=2\cos x+2$

Since $y(0)=-2$, the solution is

$y=-\sqrt{2\cos x+2}$