There is an example in a book regarding DEs which I do not understand. Solve the IVP(adsbygoogle = window.adsbygoogle || []).push({});

[tex] y'=y^2-4, y(0)=-2 [/tex]where t is the independent variable

We first solve by separation of variables to arrive at the 1-parameter solution.

[tex] -\frac{1}{4}ln (y+2)+\frac{1}{4}ln (y-2)=t+c[/tex]

Simplifying and expressing the solution explicitly, we find that,

[tex] y=2\frac{1+ce^{4t}}{1-ce^{4t}} [/tex]

Taking the initial condition,

[tex] -2=2\frac{1+c}{1-c} [/tex] which simplifies to,

-1=1.

They said that the solution is wrong because:

we can express the DE as, [tex] y'=(y+2)(y-2) [/tex] and that the when y=-2, and y=2 satisfies this equation (what does it mean?). How do we "preclude" y=-2 and y=-2 before solving starting to solve the DE?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Losing a solution of a 1st order ODE?

**Physics Forums | Science Articles, Homework Help, Discussion**