Differential Equations
Reducible to Linear Equations
Grade 12
Question:
<p>The solution of <span>\(\frac{dy}{dx}(x^2y^3 + xy) = 1\)</span> is</p>
<p>(A) <span>\(\frac{y^2}{2} - \frac{y}{x} = Ce^{\frac{y^2}{x}}\)</span></p>
<p>(B) <span>\(\frac{1}{y} - \frac{e^y}{x} = \frac{1}{2}\log(1 + 2x^2)\)</span></p>
<p>(C) <span>\(\frac{1}{y} - \frac{e^y}{2} = \frac{1}{2x^2}\)</span></p>
<p>(D) <span>\(\frac{y^2}{2} = Ce^{\frac{y^2}{x}}\)</span></p>
Step-by-Step Solution
Key Concept: Recognize equations reducible to linear form and apply substitution to transform into standard linear differential equation format.
<p>This is a differential equation reducible to linear form. Rearrange and solve using appropriate substitution techniques.</p>
Correct Answer: A