Question

The degree and order respectively of the differential equation of all the parabolas whose axis is x-axis, are

• A. $2,1$
• B. $1,2$
• C. $2,2$
• D. $1,1$

Answer 1

The correct option is B $1,2$

Equation of all parabolas whose axis is x-axis are $y^2=4a(x+c)$
Differentiating w.r.t $x$ we get $2y{y}^{\prime }=4a$
Again differentiating we get $2(y{y}^{\prime }+y^{\prime }{y}^{\prime })=0$
$\Rightarrow 2y{y}^{\prime \prime }+2{\left(y^{\prime }\right)}^2=0$
$\therefore$ degree is the natural power on highest order differential coefficient $=1$
Order is the highest order differential coefficient $=2$