Separable differential equations practice problems
Separate the variables, integrate both sides, and use the initial condition. 30 problems with worked solutions; in 30 of them every equation is proved by a computer algebra system.
Solve the initial-value problem \( \displaystyle \dfrac{dy}{dx} = - y,\ y(0) = 5 \).
Solve the initial-value problem \( \displaystyle \dfrac{dy}{dx} = y^{2},\ y(0) = \frac{1}{4} \).
Solve the initial-value problem \( \displaystyle \dfrac{dy}{dx} = - y,\ y(0) = 2 \).
Solve the initial-value problem \( \displaystyle \dfrac{dy}{dx} = y^{2},\ y(0) = \frac{1}{3} \).
Solve the initial-value problem \( \displaystyle \dfrac{dy}{dx} = y^{2},\ y(0) = 1 \).
Solve the initial-value problem \( \displaystyle \dfrac{dy}{dx} = y,\ y(0) = 4 \).
Solve the initial-value problem \( \displaystyle \dfrac{dy}{dx} = y^{2},\ y(0) = \frac{1}{2} \).
Solve the initial-value problem \( \displaystyle \dfrac{dy}{dx} = y,\ y(0) = 5 \).
Solve the initial-value problem \( \displaystyle \dfrac{dy}{dx} = \frac{3 x}{y},\ y(0) = 3 \).
Solve the initial-value problem \( \displaystyle \dfrac{dy}{dx} = 2 y,\ y(0) = 4 \).
Solve the initial-value problem \( \displaystyle \dfrac{dy}{dx} = \frac{3 x}{y},\ y(0) = 5 \).
Solve the initial-value problem \( \displaystyle \dfrac{dy}{dx} = \frac{2 x}{y},\ y(0) = 5 \).
Solve the initial-value problem \( \displaystyle \dfrac{dy}{dx} = \frac{3 x}{y},\ y(0) = 4 \).
Solve the initial-value problem \( \displaystyle \dfrac{dy}{dx} = - 2 y,\ y(0) = 3 \).
Solve the initial-value problem \( \displaystyle \dfrac{dy}{dx} = - x y,\ y(0) = 5 \).
Solve the initial-value problem \( \displaystyle \dfrac{dy}{dx} = - 3 x y,\ y(0) = 5 \).
Solve the initial-value problem \( \displaystyle \dfrac{dy}{dx} = \frac{x}{y},\ y(0) = 3 \).
Solve the initial-value problem \( \displaystyle \dfrac{dy}{dx} = 2 x y,\ y(0) = 2 \).
Solve the initial-value problem \( \displaystyle \dfrac{dy}{dx} = \frac{x}{y},\ y(0) = 1 \).
Solve the initial-value problem \( \displaystyle \dfrac{dy}{dx} = \frac{2 x}{y},\ y(0) = 2 \).
Solve the initial-value problem \( \displaystyle \dfrac{dy}{dx} = 3 x y,\ y(0) = 4 \).
Solve the initial-value problem \( \displaystyle \dfrac{dy}{dx} = \frac{3 x}{y},\ y(0) = 1 \).
Solve the initial-value problem \( \displaystyle \dfrac{dy}{dx} = 2 x y,\ y(0) = 3 \).
Solve the initial-value problem \( \displaystyle \dfrac{dy}{dx} = - 2 y,\ y(0) = 5 \).
Solve the initial-value problem \( \displaystyle \dfrac{dy}{dx} = 3 x y,\ y(0) = 2 \).
Solve the initial-value problem \( \displaystyle \dfrac{dy}{dx} = - x y,\ y(0) = 2 \).
Solve the initial-value problem \( \displaystyle \dfrac{dy}{dx} = 3 x y,\ y(0) = 5 \).
Solve the initial-value problem \( \displaystyle \dfrac{dy}{dx} = - 2 y,\ y(0) = 4 \).
Solve the initial-value problem \( \displaystyle \dfrac{dy}{dx} = - 3 x y,\ y(0) = 3 \).
Solve the initial-value problem \( \displaystyle \dfrac{dy}{dx} = - 2 x y,\ y(0) = 5 \).