Question

The differential equation representing the family curves $y^2=2c(x+\sqrt{c})$ when $c$ is a parameter is of

• A. order 4
• B. order 3
• C. order 2
• D. order 1

Answer 1

The correct option is D order 1

$y^2=2c(x+\sqrt{c})$

$\Rightarrow 2y{y}^1=2c$

$\Rightarrow y{y}^1=c$...(i)

$y^2=2y{y}^1(x+\sqrt{y{y}^1})$

$y^2=2xy{y}^1+2(y{y}^1{)}^{\frac{3}{2}}$

$(y^2-2xy{y}^1{)}^2=4(y{y}^1{)}^3$

Hence, order of differential Equation $=1$