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  4. Number of straight lines which satisfy the differential equation (d y/d x)+x((d y/d x))2-y=0 is:

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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=k x+b ; \frac{d y}{d x}=k \Rightarrow k x+b \equiv k+x^2 \Rightarrow k=k^2 \& b=k $
$k=0 \text { or } k=1 \Rightarrow \text { result }$