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Q.
Number of straight lines which satisfy the differential equation $\frac{d y}{d x}+x\left(\frac{d y}{d x}\right)^2-y=0$ is -
Differential Equations
Solution:
$y=m x+c \Rightarrow \frac{d y}{d x}=m$
It satisfies $\frac{d y}{d x}+x\left(\frac{d y}{d x}\right)^2-y=0$
$m+x m^2-m x-c=0$
$x\left(m^2-m\right)+(m-c)=0$
This is an identity so
$m=0 $ or $m=1 \& c=m$
So two such straight line are possible.