Order of differential equation whose solution is `y = cx + c^2 - 3c^(3//2) + 2`, where c is a parameter is

Options

A. 1,2
B. 2,2
C. 1,3
D. 1,4

Answer

D

Explanation

Given :
Solution of differential equation is
` y= cx +c^(2) - 3c^(3/2) +2`
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 `
` Rightarrow (y-2)^(2) + ((dy)/(dx))^(4) + (2x -9) ((dy)/(dx))^(3)`
` + (x^(2)-2y +4) ((dy)/(dx))^(2) + (-2xy +4x) (dy)/(dx) =0`
Hence order of differential equation is 1 and degree is 4.