Section 8.1 - Solving Separable Differential Equations
Exercises
Directions: You should try to solve each problem first, and then click "Reveal Answer" to check your answer. You can click "Watch Video" if you need help with a problem.
1. Find the general solution of the differential equation: \(2\sqrt{x}\,y'=\sqrt{1-y^2}\)
- \(y=\sin(\sqrt{x}+C),\quad\) equilibrium solutions at \(y=\pm1\)
2. Find the solution to the initial value problem and the interval of validity: \(2\sqrt{x}\dfrac{dy}{dx}=\cos^2 y,\qquad\) \(y(4)=\dfrac{\pi}{4}\)
\(y=\arctan(\sqrt{x}-1), \quad\)\(I.V.=(0,\infty)\)
3. In a certain culture of bacteria, the number of bacteria increases sixfold in 10hrs. How long does it take for the population to double?
Approximately 3.87 hours