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Question: Answered & Verified by Expert
The solution of the differential equation $x \frac{d y}{d x}+y=x^2+3 x+2$
MathematicsDifferential EquationsJEE Main
Options:
  • A $x y=\frac{x^3}{3}+\frac{3}{2} x^2+2 x+c$
  • B $x y=\frac{x^4}{4}+x^3+x^2+c$
  • C $x y=\frac{x^4}{4}+\frac{x^3}{3}+x^2+c$
  • D $x y=\frac{x^4}{4}+x^3+x^2+c x$
Solution:
1044 Upvotes Verified Answer
The correct answer is: $x y=\frac{x^3}{3}+\frac{3}{2} x^2+2 x+c$
$x \frac{d y}{d x}+y=x^2+3 x+2 \Rightarrow \frac{d y}{d x}+\frac{y}{x}=x+3+\frac{2}{x}$
Here $P=\frac{1}{x}, Q=x+3+\frac{2}{x}$, therefore I.F. $=e^{\int \frac{1}{x} d x}=x$ Now solve it.

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