Differential Equations Question - None

Question

Number of solutions of $\dfrac{dy}{dx}=\dfrac{y+1}{x-1}$ through $(1,0)$.

Accepted Answer

Separable: $dy/(y+1)=dx/(x-1)$ → $\ln|y+1|=\ln|x-1|+C$ → $y+1=A(x-1)$. Through $(1,0)$: $1=A\cdot 0=0$ → undefined\! The point $(1,0)$ is a singular point (both numerator and denominator zero in a special way). The constant solution $y=-1$ exists. Checking unique solutions: answer 1.

Question:

Step-by-Step Solution

Master Differential Equations with Mathbee