Differential Equations
Variable Separable Form
JEE Main PYQ
Grade 12
Question:
If $y = f(x)$ satisfies $\frac{dy}{dx} = 2x$ with $f(0) = 3$, then $f(2)$ equals _____.
Step-by-Step Solution
Key Concept: Integrate both sides with respect to $x$ to obtain the general solution $y = x^2 + C$, then use the given condition to find $C$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: 7