Find the general solution of the differential equation dy/dx=3x^2 and state its domain.

Find the general solution of the differential equation $\frac{d y}{d x} = 3 x^{2}$ and state its domain.

easy 1 mark Class 12 · Mathematics · Differential Equations

Answer

y = x^{3} + C

The correct answer is $y = x^{3} + C$ — The function $y (x)$ is defined for all real $x$ as the equation is a polynomial

Integrate both sides with respect to $x$
$\int \frac{d y}{d x}, d x = \int 3 x^{2}, d x$
$y = x^{3} + C$ because the indefinite integral of $3 x^{2}$ is $x^{3}$ plus a constant
The function $y (x)$ is defined for all real $x$ as the equation is a polynomial

Common mistake: Forgetting the constant of integration

Concept tested: First‑order separable differential equation

Published 2 September 2026 · Last updated 16 September 2026 · How this solution was prepared and checked