Differential EquationHard
Question
The integral curve through origin satisfying the differential equation y2 (3x9 + y) 
= x3(1 - 9x5y3) is-
= x3(1 - 9x5y3) is-Options
A.3(x3y)2 + y3 - x3 = 0
B.4(x3y)3 + y4 - x4 = 0
C.4(x3y)3 - y4 + x4 = 0
D.3(x3y)2 - y3 + x3 = 0
Solution
3x9y2 
+ 9x8y3 + y3 - x3 = 0
3x6y2(x3dy + 3x2ydx)+y3dy - x3dx = 0
3(x3y)2d(x3y) + y3dy - x3dx = 0
(x3y)3 +
= C
y(0) = 0 ⇒ C = 0
4(x3y)3 + y4 - x4 = 0
+ 9x8y3 + y3 - x3 = 03x6y2(x3dy + 3x2ydx)+y3dy - x3dx = 0
3(x3y)2d(x3y) + y3dy - x3dx = 0
(x3y)3 +
= Cy(0) = 0 ⇒ C = 0
4(x3y)3 + y4 - x4 = 0
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