Differential Equations
Linear ODE — particular solution check
Grade Class 12
Question:
<p>\\(\\dfrac{dy}{dx}-\\dfrac{y+3}{x+2}=0\\). The family of solutions is:</p>
<span>\(circles\)</span>
<span>\(straight lines\)</span>
<span>\(parabolas\)</span>
<span>\(hyperbolas\)</span>
Step-by-Step Solution
Key Concept: Separable ODE — solve and interpret.
<div class='solution'><p><strong>Step 1:</strong> Separable: $\dfrac{dy}{y+3}=\dfrac{dx}{x+2}$ → $\ln|y+3|=\ln|x+2|+C$ → $y+3=k(x+2)$.</p><p><strong>Step 2:</strong> This is $y=kx+(2k-3)$ — a family of <strong>straight lines</strong> through the point $(-2,-3)$. <strong>Answer: (2)</strong>.</p></div>
Correct Answer: 2