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Question

(B) Given the differential equation: $\frac{dy}{dx} = x^2 + \sin 3x$. To find the solution,we integrate both sides with respect to $x$: $y = \int (x^2

Vedclass · Accepted Answer

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

Vedclass · Answer

(B) Given the differential equation: $\frac{dy}{dx} = x^2 + \sin 3x$. To find the solution,we integrate both sides with respect to $x$: $y = \int (x^2 + \sin 3x) dx$. Using the standard integration formulas $\int x^n dx = \frac{x^{n+1}}{n+1}$ and $\int \sin(ax) dx = -\frac{\cos(ax)}{a} + c$: $y = \frac{x^3}{3} - \frac{\cos 3x}{3} + c$. Thus,the correct option is $B$.

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

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