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Calculus and Beyond Homework Help
First order Partial differential equation
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[QUOTE="Ray Vickson, post: 5479861, member: 330118"] You are being led astray by poor notation! It is better in problems such as this to avoid the ##df/dx## notation for derivatives, and use ##f'## instead. The point is that ##f'(u) = df(u)/du## is just a function of ##u##---never mind for the moment that it is a derivative. Your equation ##x^2 f'(x^3/3) = x^3## becomes ##f'(x^3/3) = x ##, or ##f'(u) = (3u)^{1/3}##. Now do ##\int f'(u) \, du## to find ##f(u)##. Then, and only then, put back ##u## in terms of ##x## and ##y##. [/QUOTE]
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First order Partial differential equation
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