Differential Equation Entry?
04-10-2018, 11:14 AM
Post: #1
 DrD Senior Member Posts: 1,132 Joined: Feb 2014
Differential Equation Entry?
How can this be solved using the prime: (Ideally, returning BOTH a general and a particular solution.)

(y*e^x) dx + (y^2 - 1) dy = 0, AND y(0) = 1

Desired results:
y^2 - ln(y^2) = -2*e^x + c1; {General Solution}
y^2 - ln(y^2) = -2*e^x + 3; {Particular solution}
04-10-2018, 11:53 AM
Post: #2
 parisse Senior Member Posts: 1,178 Joined: Dec 2013
RE: Differential Equation Entry?
desolve(y*exp(x)+(y^2-1)*y'=0) returns the implicit equation for the solutions (in display and if you interpret fsolve).
odesolve will solve this equation numerically, but not for this initial condition, because Cauchy-Lipschitz is not verified if y=1 (you can not express y' in terms of x and y).
04-10-2018, 01:22 PM
Post: #3
 DrD Senior Member Posts: 1,132 Joined: Feb 2014
RE: Differential Equation Entry?
(04-10-2018 11:53 AM)parisse Wrote:  desolve(y*exp(x)+(y^2-1)*y'=0) returns the implicit equation for the solutions (in display and if you interpret fsolve).
odesolve will solve this equation numerically, but not for this initial condition, because Cauchy-Lipschitz is not verified if y=1 (you can not express y' in terms of x and y).

Thanks, Bernard! I tried lots of other ways, but not that one, and I spent way too much time trying them!

-Dale-
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