Solving a first order differential equation (calculus 1)

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SUMMARY

The discussion focuses on solving the first order differential equation dy/dx = y - e^(-x). The correct solution is y = c * e^(x) + 0.5 * e^(-x), as confirmed by Wolfram Alpha. The key steps involve rearranging the equation into the standard form dy/dx + p(x)y = q(x) and finding an integrating factor. The participant initially struggled with the solution but successfully resolved it after guidance.

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  • Understanding of first order differential equations
  • Familiarity with integrating factors
  • Knowledge of exponential functions
  • Basic calculus concepts
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  • Explore the use of Wolfram Alpha for solving differential equations
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Students studying calculus, particularly those focusing on differential equations, as well as educators looking for practical examples of solving first order differential equations.

myeviltacos
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Homework Statement



dy/dx=y-e-x

Homework Equations



none

The Attempt at a Solution



According to Wolfram Alpha the solution is y = cex+.5e-x . I tried multiple approaches, but I cannot obtain this answer. I can't figure out what step 1 is.

I tried factoring out e-x from the right side of the equation, but I couldn't go anywhere from there, and factoring out y did not work either.
 
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First rearrange it to dy/dx + p(x) y = q(x), where p(x) and q(x) are arbitrary functions. Then find an integrating factor.
 
Char. Limit said:
First rearrange it to dy/dx + p(x) y = q(x), where p(x) and q(x) are arbitrary functions. Then find an integrating factor.

Oh wow, thanks for your response. I solved it. :)
 

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