The differential equation whose solution represents the family $x^2 y=4 \mathrm{e}^x+\mathrm{c}$, where c is an arbitrary constant, is
- A$\quad x \frac{\mathrm{~d} y}{\mathrm{~d} x}+x y=0$
- B$\quad x^2 \frac{\mathrm{~d} y}{\mathrm{~d} x}+(2 x-x y)=0$
- C$x \frac{\mathrm{~d} y}{\mathrm{~d} x}+(x-2) y=0$
- D$x^2 \frac{\mathrm{~d} y}{\mathrm{~d} x}+2 x y-4 \mathrm{e}^x=0$
✓ Correct answer: D
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