Question

Find the curve passing through the point (0, 1) and satisfying the equation sin $\left(\frac{dy}{dx}\right)=a$

Answer 1

$\sin \left(\frac{dy}{dx}\right)=a$

$\therefore \frac{dy}{dx}={\sin }^{-1}a$

$\therefore \int dy={\sin }^{-1}a\int dx$

$\therefore y=x{\sin }^{-1}a+c$

When $x=0,y=1$

hence $c=1$

$\therefore y=x{\sin }^{-1}a+1$

$\therefore \frac{y-1}{x}={\sin }^{-1}a$

$\therefore \sin \left(\frac{y-1}{x}\right)=a$