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Homework Statement
The differential equation dy/dx= 35/(y1/8+25x2y1/8 has an implicit general solution of the form F(x,y)=K. In fact, because the differential equation is separable, we can define the solution curve implicitly by the form F(x)=G(x)+H(y)=K.
Find such solution and then give the related functions requested.
Homework Equations
The Attempt at a Solution
dy/dx=35/(y1/8(1+25x2)
1+25x2/35 dx=y1/8dy
1/35[tex]\int1+25x^2 dx[/tex]=[tex]\int y^(1/8) dy[/tex]
x+25x3/105=8/9y9/8
105(8/9y9/8)-x-253=K
so G(x)=x+25x3 and H(y)=8/9y9/8