Mathematics - Differential Equation Question with Solution | TestHub

$$\begin{array}{rl}& y^2=2c(x+\sqrt{c}).....(i)\\ & 2y{y}^{\prime }=2c\cdot 1\text{ or }y{y}^{\prime }=c....(ii)\\ & \Rightarrow y^2=2y{y}^{\prime }\left(x+\sqrt{y{y}^{\prime }}\right)\end{array}$$ [on putting value of c from (ii) in (i)] On simplifying, we get $${\left(y-2x{y}^{\prime }\right)}^2=4y{y}^{\prime 3}.....(iii)$$ Hence equation (iii) is of order 1 and degree 3.