Seperable Equation, Differential Equations, Can't Seperate

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SUMMARY

The discussion centers on solving the differential equation dy/dt - 2ty = 9(t^2)e^(t^2) with the initial condition y(0)=1. The solution requires the use of an integrating factor, which was initially overlooked by the user. After applying the integrating factor method, the user successfully solved the equation, highlighting the importance of recognizing when to use this technique in non-separable differential equations.

PREREQUISITES
  • Understanding of first-order differential equations
  • Knowledge of integrating factors in differential equations
  • Familiarity with exponential functions and their properties
  • Basic calculus concepts, including differentiation and integration
NEXT STEPS
  • Study the method of integrating factors in detail
  • Practice solving non-separable differential equations
  • Explore applications of differential equations in real-world scenarios
  • Learn about other techniques for solving differential equations, such as separation of variables and exact equations
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Students and educators in mathematics, particularly those focusing on differential equations, as well as anyone seeking to improve their problem-solving skills in this area.

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Homework Statement




dy/dt - 2ty = 9(t^2)e^(t^2)


Find y(t) that satisfies this equation for y(0)=1.

Homework Equations





The Attempt at a Solution



I added 2ty, multiplied by dt, but after that, I cannot separate y and t. Any help? Thank you for looking.
 
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With an equation like that, you need to multiply by an integrating factor. Check here for more information on it.
 
I solved it, thank you. I had worked 4 equations that were set up to be seperable before that one, so I didn't think to try an integrating factor. Thanks for the help.
 

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