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  • The general solution of frac{d y}{d x}=2 x e^{x^{2}-y} is (a) e^{x^{2}-y}=c

The general solution of \frac{d y}{d x}=2 x e^{x^{2}-y} is
(a) e^{x^{2}-y}=c
(b)  e^{-y}+e^{x^{2}}
(c) e^{y}=e^{x^{2}}+c
(d) e^{x^{2}+y}=c

Answers (1)

The answer is the option (c)

Explanation: -

\begin{aligned} &\begin{array}{ll} \Rightarrow & e^{y} \frac{d y}{d x}=2 x e^{x^{2}} \\ \Rightarrow & \int e^{y} d y=2 \int x e^{x^{2}} d x \end{array}\\ &\text { Put } x^{2}=t \text { in } \mathrm{R} \text { . H.S. integral, we get }\\ &2 x d x=d t\\ &\begin{array}{ll} \Rightarrow & \int e^{y} d y=\int e^{t} d t \\ \Rightarrow & e^{y}=e^{t}+C \\ \Rightarrow & e^{y}=e^{x^{2}}+C \end{array} \end{aligned}

 

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