Differential Equations
Separable ODE
Grade Class 12
Question:
<p>\\(\\dfrac{dy}{dx}=\\dfrac{2y}{x}\\), \\(y(1)=1\\). The curve is:</p>
<span>\(y = x^2 \text{ (parabola)}\)</span>
<span>\(y = x^3\)</span>
<span>\(y = x^{1/2}\)</span>
<span>\(y = x\)</span>
Step-by-Step Solution
Key Concept: Separable: dy/y = 2dx/x.
<div class='solution'><p>$\int dy/y=2\int dx/x$ → $\ln y=2\ln x+C$ → $y=Ax^2$. With $y(1)=1$: $A=1$. $y=x^2$. <strong>Answer: (1)</strong>.</p></div>
Correct Answer: 1