Question

The solution of the differential equation \(\displaystyle \frac{dy}{dx}+\frac{y}{x}=x^2\) under the condition that \(y(1)=1\) is

• A. \(4xy=x^3+3\)
• B. \(4xy=x^4+3\)
• C. \(4xy=x^3-3\)
• D. \(4xy=x^4-3\)

Hint:

For \(\frac{dy}{dx}+P(x)y=Q(x)\), use integrating factor \(e^{\int P(x)\,dx}\). Here the integrating factor is \(x\).

Answer 1

The Correct Option is B