Question

The solution of the differential equation $\frac{dy}{dx} = x^{2} + \sin 3x$ is

• A. $y = \frac{x^{3}}{3} + \frac{\cos 3x}{3} + c$
• B. $y = \frac{x^{3}}{3} - \frac{\cos 3x}{3} + c$
• C. $y = \frac{x^{3}}{3} + \sin 3x + c$
• D. None of these

Answer 1

Answer: (B)

$y = \frac{x^{3}}{3} - \frac{\cos 3x}{3} + c$

Answer 2

We have $dy = (x^{2} + \sin 3x)dx$ ⇒ $\int_{}^{}{dy = \int_{}^{}{(x^{2} + \sin 3x)dx}}$ ⇒ $y = \frac{x^{3}}{3} - \frac{\cos 3x}{3} + c$