Question

The differential equation representing the family of curves $y^2=a(ax+b)$ where $a$ and $b$ are arbitrary constants, is of

• A. order 1,degree 1
• B. order 1,degree 3
• C. order 2,degree 3
• D. order 1,degree 4
• E. order 2,degree 1

Answer 1

Answer: (E)

order 2,degree 1

we have $y^2=a(ax+b)$
$\Rightarrow y^2=a^{2}x+ab$
On differentiating w.r.t $x$ we get
$2y\frac{dy}{dx}=a^2$
$\Rightarrow y\frac{dy}{dx}=\frac{a^2}{2}$
$\Rightarrow y\frac{d^{2}y}{d{x}^2}+\frac{dy}{dx}.\frac{dy}{dx}=0$
$y.y_2+{\left(y_1\right)}^2=0$
Hence order and degree of the given equation is $2$ and $1$, respectively