Separable equations

What the problems look like

A few statements from this skill. Answers, hints and worked solutions live in the practice session.

1. Warm-up

   Separating variables in $\dfrac{dy}{dx} = \sqrt{1-y^{2}}$ (with $-1 \le y \le 1$) gives the family of solutions $\arcsin y = x + C$. Find the constant $C$ for the member of this family that passes through the point $(4, -1/2)$.

2. Warm-up

   Separating variables in $\dfrac{dy}{dx} = \sqrt{1-y^{2}}$ (with $-1 \le y \le 1$) gives the family of solutions $\arcsin y = x + C$. Find the constant $C$ for the member of this family that passes through the point $(1, -1/2)$.

3. Warm-up

   Separating variables in $\dfrac{dy}{dx} = \sqrt{1-y^{2}}$ (with $-1 \le y \le 1$) gives the family of solutions $\arcsin y = x + C$. Find the constant $C$ for the member of this family that passes through the point $(3, 1)$.

Problems shown under their original terms: Generated (template, solver-computed).