# Thread: [SOLVED] first order equation

1. ## [SOLVED] first order equation

Hello,
I have to solve such equation:
$y'-y+y^2e^{2x}=0$
I thought about two substitutions. First t=1/y, and after that t=uv, but after doing that lot of calculations I still do not get right result. Is there any faster and more reliable method?
V.

2. Originally Posted by Vermax
Hello,
I have to solve such equation:
$y'-y+y^2e^{2x}=0$
I thought about two substitutions. First t=1/y, and after that t=uv, but after doing that lot of calculations I still do not get right result. Is there any faster and more reliable method?
V.
This is a Bernoulli equation:
$\frac {dy}{dx} + P(x) y = Q(x) y^n$

where $P(x) = -1$ and $Q(x) = -e^{2x}$ and $n=2$.

Putting $t = 1/y$ is the substitution you want. Then you should be able to put it in the form:

$\frac {dt}{dx} = (1-n) P(x) t = (1-n) Q(x)$

where $P, Q, t$ are as above.

You should then be able to solve it using an integrating factor, I expect.

3. Just wanted to thank you for your answer and confirmation. Equation solved