Welcome to your Differential Equations Quiz 1
1. Order and Degree (if defined) of a differential equation are always positive integers.
2. Which of the following is free from arbitrary constants?
3. Which of the following is not a homogeneous differential equation?
4. For a differential equation of the form $ \frac{dy}{dx} + Py = Q $, where P and Q are functions of x or constants, the Integrating factor (I.F.) is given by
5. Write the sum of the order and degree of the differential equation: $(\frac{d^2y}{dx^2})^2 + (\frac{dy}{dx}) + x^4 = 0 $ ?
6. For a differential equation of the form $ \frac{dx}{dy} + Px = Q $, where P and Q are functions of y or constants, the solution is given by
7. What is the degree of the differential Equation: $ \sqrt{1 + \frac{dy}{dx}} =(\frac{d^2y}{dx^2})^{\frac{1}{3}} $ ?
8. What is the order and degree of the differential equation $ \frac{d^5y}{dx^5} + \log {\frac {dy}{dx}} $ ?
9. If the differential equation of the form $\frac{dy}{dx} = F(x, y)$ is a homogenous differential Equation. Then $F(x, y)$ is a homogenous function of degree ___
10. The following differential equation is of which form: $e^x \tan y dx + (1-e^x) \sec^2 y dy = 0 $
