Differential Equation With Subsitution

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SUMMARY

The discussion focuses on solving the differential equation (y^2)(y'')=y' using substitution techniques. The user successfully substituted v for y' and v*(dv/dy) for y'', leading to the equation dy/dx=-1/y+C. This equation is confirmed to be separable and can be easily integrated to find the solution. The key takeaway is the importance of recognizing separable equations in the context of differential equations.

PREREQUISITES
  • Understanding of differential equations and their classifications
  • Familiarity with substitution methods in calculus
  • Knowledge of integration techniques for separable equations
  • Basic concepts of derivatives and their notation
NEXT STEPS
  • Study the method of substitution in solving differential equations
  • Learn about separable differential equations and their integration
  • Explore advanced techniques for solving higher-order differential equations
  • Review examples of integrating factors in differential equations
USEFUL FOR

Students studying calculus, particularly those focusing on differential equations, as well as educators looking for examples of substitution methods in solving such equations.

Moragor
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Homework Statement


I have to solve (y^2)(y'')=y' using substitution.


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The Attempt at a Solution


I substituted in v for y' and v*(dv/dy) for y'' and then I got stuck at dy/dx=-1/y+C. Am I doing this wrong, or am I just missing how to solve that second equation?
 
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You're doing it right. That equation that you've ended up with is seperable and easy to integrate.
 

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