I am trying to solve the following ODE in order to obtain a solution in explicit for:
xdy=(x+y)dx
WITH INITIAL CONDITION Y(X=0)=-2
i have tried exact equations and attempted substituion but no luck.
thanks
I am trying to solve the following ODE in order to obtain a solution in explicit for:
xdy=(x+y)dx
WITH INITIAL CONDITION Y(X=0)=-2
i have tried exact equations and attempted substituion but no luck.
thanks
@OP: To expand, the DE can be written $\displaystyle \displaystyle \frac{dy}{dx} = 1 + \frac{y}{x}$ (provided $\displaystyle x \neq 0$). I suppose the given initial condition might be a limit, as in $\displaystyle \displaystyle \lim_{x \to 0} y = -2$ .... But that condition is false in fact false since $\displaystyle \displaystyle \lim_{x \to 0} y = 0$ ....
The substitution $\displaystyle y=vx$ ( homogeneous equation ) provides the general solution:
$\displaystyle y=x(C+\log |x|)$
Possibly there is a typo and the initial condition is $\displaystyle y(1)=-2$ , so the particular solution would be:
$\displaystyle y=x(-2+\log |x|)$
Fernando Revilla