What are the order and degree respectively of the differential equation whose solution is y = cx + c ^2-3 c ^ 3 / 2 +2 , where c is a parameter?

Step-by-step solution

Given : Solution of differential equation is y=c x+c^2-3 c^ 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 d y d x =c aligned & y=x d y d x + ( d y d x )^2-3 ( d y d x )^ 3 2 +2 & (y-2)^2+ ( d y d x )^4+(2 x-9) ( d y d x )^3 aligned + (x^2-2 y+4 ) ( d y d x )^2+(-2 x y+4 x) d y d x =0 Hence order of differential equation is 1 and degree is 4 .