I wanna solution for this problem

Thread starter boshoof
Start date Oct 24, 2006

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SUMMARY

The discussion focuses on solving the differential equation xy' = [(x^2 - y^2)]^1/2. A key insight provided is the suggestion to divide through by x, allowing the equation to be expressed as a function of y/x. This transformation leads to a separable equation, which simplifies the process of finding a complete solution. The importance of substitution in solving such equations is emphasized as a critical step.

PREREQUISITES

Understanding of differential equations
Familiarity with separable equations
Knowledge of substitution methods in calculus
Basic algebraic manipulation skills

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Study the method of solving separable differential equations
Learn about substitution techniques in calculus
Explore examples of differential equations with variable separation
Review the properties of functions and their transformations

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Students and professionals in mathematics, particularly those studying calculus and differential equations, as well as educators seeking to enhance their teaching methods in these areas.

Oct 24, 2006

boshoof

i want to a complete solution for this problem please
xy'=[(x^2-y^2)]^1/2

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Oct 24, 2006

HallsofIvy

Science Advisor

Homework Helper

Yeah, and I want a lot of things I can't have! What have you tried yourself? (Did you notice that if you divide through by x, you can write the right hand side as a function of y/x? A simple substitution makes it a separable equation.)