- #1
vish_maths
- 61
- 1
The question comprises of three subparts which need to be converted to Clairaut's form and then solved :
(a) x p2 - 2yp + x + 2y = 0
(b) x2 p2 + yp (2x + y) + y2 = 0
(c) (x2+y2)(1+p)2-2(x+y)(1+p)(x+yp)+(x+yp)2=0
Note : p = dy/dx
I understand that Reducing to Clairaut's form involves suitable substitution so as to bring it in the form of V = P U + f(P) but i am unable to form any intuition about what such substitutions might be , as the above equations seem complicated with more than one combination of variables and 'p'.
I have added three sub-parts to get a better understanding of the intuition involved in such substitutions. Help would be greatly appreciated. Thanks.
(a) x p2 - 2yp + x + 2y = 0
(b) x2 p2 + yp (2x + y) + y2 = 0
(c) (x2+y2)(1+p)2-2(x+y)(1+p)(x+yp)+(x+yp)2=0
Note : p = dy/dx
I understand that Reducing to Clairaut's form involves suitable substitution so as to bring it in the form of V = P U + f(P) but i am unable to form any intuition about what such substitutions might be , as the above equations seem complicated with more than one combination of variables and 'p'.
I have added three sub-parts to get a better understanding of the intuition involved in such substitutions. Help would be greatly appreciated. Thanks.