Differential Equations
Exact Differential Equations
Grade 12
Question:
<p>Solution of the differential equation \(e^{x^2}(y^2 - 1)dy + e^{y^2} - y dy + e^{x^2}(xy^2 - x) = 0\) is</p>
<p>(A) \(e^{x^2}(y^2 - 1) + e^{y^2} = C\)</p>
<p>(B) \(e^{y^2}(x^2 - 1) + e^{x^2} = C\)</p>
<p>(C) \(e^{y^2}(y^2 - 1) + e^{x^2} = C\)</p>
<p>(D) \(e^{x^2}(y - 1) + e^{y^2} = C\)</p>
Step-by-Step Solution
Key Concept: Recognize the exact differential equation form and integrate both sides to obtain the solution.
<p>Rearranging the differential equation and separating variables to identify the exact differential form yields the solution.</p>
Correct Answer: A