Exam Questions & Step-by-Step Markschemes (145 Problems)
Question 1 • 2022
2 Marks
Find the sum of the order and the degree of the differential equation : \left(x + \frac{dy}{dx}\right)^2 = \left(\frac{dy}{dx}\right)^2 + 1
Answer: 2
Question 2 • 2022
3 Marks
Find the particular solution of the differential equation x\frac{dy}{dx} + x\cos^2\left(\frac{y}{x}\right) = y ; given that when x = 1 , y = \frac{\pi}{4} .
Answer: \tan\left(\frac{y}{x}\right) = 1 - \log|x|
Question 3 • 2022
2 Marks
Solve the differential equation : \log\left(\frac{dy}{dx}\right) = x - y .
Answer: e^y = e^x + C
Question 4 • 2022
3 Marks
Solve the differential equation : \frac{dy}{dx} = \frac{x^2 + y^2}{xy} .
Answer: y^2 = 2x^2\log|x| + Cx^2
Question 5 • 2022
2 Marks
Find the product of the order and the degree of the differential equation \left[\frac{d}{dx}(xy^2)\right] \cdot \frac{dy}{dx} + y = 0 .
Answer: 2
Question 6 • 2022
3 Marks
Find the particular solution of the differential equation (y + 3x^2)\frac{dx}{dy} = x , given that y = 1 , when x = 1 .
Answer: y = 3x^2 - 2x