$y=m x+\frac{2}{m}$ is the general solution of
$y=m x+\frac{2}{m}$ is the general solution of
- $y\left(\frac{d y}{d x}\right)^{2}=x\left(\frac{d y}{d x}\right)+2$
- $y=x \frac{d y}{d x}+2$
- $y\left(\frac{d y}{d x}\right)=x\left(\frac{d y}{d x}\right)^{2}+2$
- $y\left(\frac{d y}{d x}\right)=x+2$
Solution
$\begin{array}{l}
\text {Given } \mathrm{y}=\mathrm{m} \mathrm{x}+\frac{2}{\mathrm{~m}}....(1) \\
\therefore \frac{\mathrm{d} \mathrm{y}}{\mathrm{dx}}=(\mathrm{m} \times 1)+0 \Rightarrow \mathrm{m}=\frac{\mathrm{dy}}{\mathrm{dx}}
\end{array}$
Putting value of $m$ in equation (1), we get
$y=x \frac{d y}{d x}+\frac{2}{\left(\frac{d y}{d x}\right)} \Rightarrow y \frac{d y}{d x}=x\left(\frac{d y}{d x}\right)^{2}+2$
Asked in: MHT CET 2020 (14 Oct Shift 2)
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