A) \[\frac{dy}{dx}+x{{y}^{2}}=1\]
B) \[{{x}^{2}}\frac{dy}{dx}+y={{e}^{x}}\]
C) \[\frac{dy}{dx}+3y=x{{y}^{2}}\]
D) \[x\frac{dy}{dx}+{{y}^{2}}=\sin x\]
Correct Answer: B
Solution :
\[{{x}^{2}}\frac{dy}{dx}+y={{e}^{x}}\] can be written as \[\frac{dy}{dx}+\frac{y}{{{x}^{2}}}=\frac{{{e}^{x}}}{{{x}^{2}}}\], which is a linear equation.
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