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  1. C

    Nonlinear ODE by an infinite series expansion

    Okay,when I use a riccati substitution I get \frac{d^2u}{dx^2} - x^2u = 0 But now how to solve this? If I use a series expansion on this I get a solution, but it has a rather ugly recurrence relation. Maybe there is another way to solve this particular ODE, and I am totally brain farting...
  2. C

    Nonlinear ODE by an infinite series expansion

    I had done it the way suggested by loveequation, and you do end up with a pattern after you equate for the x^2 coefficient. I spent a couple of hours trying to find another way and was unsuccessful. The recurrence relation we obtain for the coefficients is not nice at all, but would be...
  3. C

    Who can find the solution to this ODE?

    I had not thought of turning it into a Bernoulli equation. Actually though I found out another, more elementary way of doing it using exact differentials: \[ \frac{dy}{dx} = \frac{x^2y^2 - y}{x} \Rightarrow x dy = x^2y^2 dx - y dx \] Divide through by y^2 \[ x\frac{1}{y^2} dy = x^2...
  4. C

    Who can find the solution to this ODE?

    Looking for the solution to the following ODE: \[ \frac{dy}{dx} = \frac{x^2y^2 - y}{x} \]
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