Calc 2: Problems with an ODE

[icedpolonium]

Hello

I'm having difficulties with the following differential equation:
$\displaystyle y'={e^{x^2}}\log(y-2)$

I tried to solve it by separating the variables ($\displaystyle y>2, y \neq 3$):

$\displaystyle \frac{\partial y}{\partial x}={e^{x^2}}\log(y-2)$
$\displaystyle \frac{\partial y}{\partial x}\frac{1}{\log(y-2)}={e^{x^2}}$

and then I'm stuck after trying to integrate both sides with respect to x:

$\displaystyle \int \frac{\partial y}{\log(y-2)}=\int {e^{x^2}} \partial x$

In fact, I can't integrate even one of them


If it is of any help, the ODE was part a Cauchy problem, with $\displaystyle y(0)=3$ being the condition to satisfy.


Am I missing something?

 

[Deleted member 4993]

Hello

I'm having difficulties with the following differential equation:
$\displaystyle y'={e^{x^2}}\log(y-2)$

I tried to solve it by separating the variables ($\displaystyle y>2, y \neq 3$):

$\displaystyle \frac{\partial y}{\partial x}={e^{x^2}}\log(y-2)$
$\displaystyle \frac{\partial y}{\partial x}\frac{1}{\log(y-2)}={e^{x^2}}$

and then I'm stuck after trying to integrate both sides with respect to x:

$\displaystyle \int \frac{\partial y}{\log(y-2)}=\int {e^{x^2}} \partial x$

In fact, I can't integrate even one of them


If it is of any help, the ODE was part a Cauchy problem, with $\displaystyle y(0)=3$ being the condition to satisfy.


Am I missing something?

let z = log(y-2) → y-2 = e^z

dy/dx = e^z * dz/dx

e^z * dz/dx * z = e^{x^2}

Now you should know

integral e^(x^2) dx = 1/2 sqrt(pi) erfi(x)+constant

and continue..