Let y_1(x), y_2(x) solve dydx=x+y with y_1(0)=0, y_2(0)=1.

Question

Let $y_1(x)$, $y_2(x)$ solve $\dfrac{dy}{dx}=x+y$ with $y_1(0)=0$, $y_2(0)=1$. The number of points of intersection of $y_1,y_2$ is:

Accepted Answer

With $t=x+y$: $\dfrac{dt}{dx}-1=t \implies |t+1|=Ce^x$, i.e. $|x+y+1|=Ce^x$.

$y_1$: $C=1$; $y_2$: $C=2$. Intersection needs $e^x=2e^x$, impossible --- no intersection.

Solutions · 1