Question

Solve the given differential equation $\frac{dy}{dx}=(cosx-sinx),$

• A. $y=sinx+cosx+c$
• B. $y=sinx-cosx+c$
• C. $y=tanx+secx$
• D. $\text{None of these}$

Answer 1

Answer: (A)

$y=sinx+cosx+c$

Given

$\frac{dy}{dx}=\cos x-\sin x$

$dy=(\cos x-\sin x)dx$

Integrating on Both sides

$\int dy=\int (\cos x-\sin x)dx$

$y=\int \cos xdx-\int \sin xdx$

$y=\sin x+\cos x+c$