Solving nonlinear first order DE w/ fractional exponents

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SUMMARY

The discussion centers on solving the nonlinear first-order differential equation (DE) given by y' + p y^(1/2) = q, where p and q are constants. The user initially attempted to apply Bernoulli's method but encountered issues due to an initial condition of t=0, y=0, leading to an undefined result. Suggestions were made to explore numerical methods or utilize Wolfram Alpha for a more manageable solution, as the analytical solution proved too complex for the user's college differential equations class.

PREREQUISITES
  • Understanding of first-order differential equations
  • Familiarity with Bernoulli's method for solving DEs
  • Basic knowledge of numerical methods for differential equations
  • Experience using computational tools like Wolfram Alpha
NEXT STEPS
  • Research numerical methods for solving nonlinear differential equations
  • Learn about the application of Wolfram Alpha for solving differential equations
  • Explore alternative methods for solving first-order DEs, such as the method of integrating factors
  • Investigate the implications of initial conditions on the solvability of differential equations
USEFUL FOR

Students and educators in mathematics, particularly those studying differential equations, as well as anyone seeking to understand the complexities of nonlinear DEs and their solutions.

hotwheelharry
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Hello. I have simple DE

y' + p y^(1/2) = q
---------------
y'=dy/dt
p,q=constant

I am confused because I tried bernoulli's method to solve and I think I exploded the universe.
Basically, my initial condition of t=0,y=0 made infinity, not right. I'm not sure that method works when there is no y^(1) with q anyway.

Any other suggestions to solve?
 
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hotwheelharry said:
Hello. I have simple DE

y' + p y^(1/2) = q
---------------
y'=dy/dt
p,q=constant

I am confused because I tried bernoulli's method to solve and I think I exploded the universe.
Basically, my initial condition of t=0,y=0 made infinity, not right. I'm not sure that method works when there is no y^(1) with q anyway.

Any other suggestions to solve?

Do you need an analytic answer or can you use a computer to show it's behaviour through a numeric scheme? Also did you try wolfram alpha?
 
Haha, totally forgot about wolfram alpha. sooo good. Anyway the solution it gave me is way to complex for my college DEQ class. I should probably change my equation. Thanks anyways.
 
Hello,

Solutionof the ODE in attachment :
 

Attachments

  • ODE LambertW.JPG
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