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The documents you've uploaded contain a quiz on differential equations with the following tasks:

1. **Determine if the given function or relationship is an explicit or implicit solution of the equation.**
2. **Verify that \( y = c x^3 \) is a one-parameter family of solutions for the equation \( \frac{dy}{dx} = \frac{3y}{x} \).**
3. **For the differential equation \( \frac{dy}{dx} = \frac{xy}{x^2 - 1} \), show that the family \( x^2 + cy^2 = 1 \) is a solution for any arbitrary \( c \), and verify that \( y = 0 \) is a singular solution**[【source】](undefined "undefined")[【source】](undefined "undefined").

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1. What is the difference between explicit and implicit solutions of differential

Determine if the given function or relationship is an explicit or implicit solution of the equation, verify that y = cx^3 is a one-parameter family of solutions for dy/dx = 3y/x, and show that x^2 + cy^2 = 1 is a solution for any arbitrary c for the differential equation dy/dx = xy/(x^2 - 1), verifying that y = 0 is a singular solution.

Explore key differential equation concepts such as implicit vs explicit solutions, one-parameter family of solutions for dy/dx = 3y/x, and the solution x^2 + cy^2 = 1 for dy/dx = xy/(x^2 - 1), verifying that y = 0 is a singular solution. Suitable for university students.

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