Question

find the partial solution of differential equation sinxdx=-dy if y=2 at x=0​

Answer 1

$\sin(x) dx = -dy$

$\frac{dy}{dx} = -\sin(x)$

$y = -\int \sin(x) dx = C - (-\cos(x)) = C + \cos(x)$

$y(0) = 2$

$y(0) = C + \cos(0) = 2$

$C + 1 = 2$

$C = 2 - 1 = 1$

$y = 1 + \cos(x)$.

Ответ. y = 1 + cos(x).