Differential Equations
Separable Equations
Grade 12
Question:
<p>The solution of <span>\(\frac{dy}{dx} = \frac{xe^{(n-1)y}}{x}\)</span> is</p>
<p>(A) <span>\(\frac{1}{n-1}\log\frac{e^{(n-1)y}}{e^{(n-1)y} - 1} = (n-1)y + C\)</span></p>
<p>(B) <span>\(e^{(n-1)y} = Ce^{(n-1)y} + (n-1)\frac{x^2}{2}\)</span></p>
<p>(C) <span>\(\log\frac{e^{(n-1)y} - 1}{(n-1)e^{(n-1)y}} = (n-1)y + x + C\)</span></p>
<p>(D) <span>\(e^{(n-1)y} = Ce^{(n-1)y} + (n-1)\frac{x^2}{2}\)</span></p>
Step-by-Step Solution
Key Concept: Recognize separable equations and use variable separation followed by integration on both sides.
<p>This is a separable differential equation. Separate variables and integrate both sides to obtain the solution.</p>
Correct Answer: B