MHT CET · Maths · Differential Equations
The integrating factor of the differential equation \(\frac{d y}{d x}+\frac{1}{x} y=x^{3}-3\) is
- A \(-y\)
- B \(y\)
- C \(x\)
- D \(-x\)
Answer & Solution
Correct Answer
(C) \(x\)
Step-by-step Solution
Detailed explanation
\(\frac{d y}{d x}+\frac{1}{x} y=x^{3}-3 \quad\) is linear differentiatial equation
\(\therefore \text { I.F. }=\mathrm{e}^{\int \frac{1}{x} \mathrm{dx}}=\mathrm{e}^{\log x}=\mathrm{x}\)
\(\therefore \text { I.F. }=\mathrm{e}^{\int \frac{1}{x} \mathrm{dx}}=\mathrm{e}^{\log x}=\mathrm{x}\)
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