Given: Solution of differential equation is y=cx+c2−3c
3
2
+2...(1) To find order and degree of differential equation, we will find differential equation first Now differentiating equation (1) w.r.t. x and putting value of c to remove it, we get
dy
dx
=c
y=x
dy
dx
+(
dy
dx
)2−3(
dy
dx
)
3
2
+2 ⇒(y−2)2+(
dy
dx
)4+(2x−9)(
dy
dx
)3 +(x2−2y+4)(
dy
dx
)2+(−2xy+4x)
dy
dx
=0
Hence order of differential equation is 1 and degree is 4.