The differential equation $y\frac{dy}{dx}+x=C$ represents
Answer & explanation
Correct answer: option 4
The correct answer is option (4) : a family of circles whose centres are on x-axis
We have,
$y\frac{dy}{dx}+x=C$
$⇒y\, dy +(x-C)dx=0$
$⇒\frac{y^2}{2}+\frac{(x-C)^2}{2}=C_1$
$⇒(x-C)^2 +y^2 =2C_1$
Clearly, it represents a family of circles having their centres on x-axis.