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

Question

Number of straight lines which satisfy the differential equation (d y/d x)+x((d y/d x))2-y=0 is - (A) 1 (B) 2 (C) 3 (D) 4

Tardigrade Admin · Accepted Answer

y=m x+c ⇒ (d y/d x)=m It satisfies (d y/d x)+x((d y/d x))2-y=0 m+x m2-m x-c=0 x(m2-m)+(m-c)=0 This is an identity so m=0 or m=1 c=m So two such straight line are possible.

Q. Number of straight lines which satisfy the differential equation $\frac{d y}{d x} + x (\frac{d y}{d x})^{2} - y = 0$ is -

1

2

3

4

$y = m x + c \Rightarrow \frac{d y}{d x} = m$
It satisfies $\frac{d y}{d x} + x (\frac{d y}{d x})^{2} - y = 0$
$m + x m^{2} - m x - c = 0$
$x (m^{2} - m) + (m - c) = 0$
This is an identity so
$m = 0$ or $m = 1& c = m$
So two such straight line are possible.

Q. Number of straight lines which satisfy the differential equation dxdy​+x(dxdy​)2−y=0 is -

1

2

3

4

y=mx+c⇒dxdy​=m It satisfies dxdy​+x(dxdy​)2−y=0 m+xm2−mx−c=0 x(m2−m)+(m−c)=0 This is an identity so m=0 or m=1&c=m So two such straight line are possible.

Q. Number of straight lines which satisfy the differential equation $\frac{d y}{d x} + x (\frac{d y}{d x})^{2} - y = 0$ is -

$y = m x + c \Rightarrow \frac{d y}{d x} = m$
It satisfies $\frac{d y}{d x} + x (\frac{d y}{d x})^{2} - y = 0$
$m + x m^{2} - m x - c = 0$
$x (m^{2} - m) + (m - c) = 0$
This is an identity so
$m = 0$ or $m = 1& c = m$
So two such straight line are possible.