Tiêu đề T1 CALENG3 LQ1 2025-2026.pdf ✅

1 To download reviewers and avail tutorials, visit: https://dlsu-syntax.vercel.app/ Society of Young Engineers Towards Achieving Excellence Tutorials | Reviewers CALENG3 Long Quiz 1 Coverage:Variable Separable and Linear DE Homogenous and Exact DE Substition Methods for solving DE I. Multiple Choice 1. An ordinary differential equation, M(x, y)dx + N(x, y)dy = 0, is ______ if it satisfies the condition ∂M ∂y = ∂N ∂x . a. Linear b. Exact c. Homogenous d. Variable Separable 2. A function f(x, y) is said to be ______ if it satisfies the condition: f(tx,ty) = t αf(x, y). a. Linear b. Exact c. Homogenous d. Variable Separable 3. Determine the integrating factor to be used in the following equation: dy dx − 4x3y = x3 a. e12x2 b. e−12x2 c. ex4 d. e−x4 4. Determine whether the function is homogenous or not. If homogenous, state the degree. f(x, y) = xy3 lnx2 2 − xy3lny a. Not Homogenous b. Homogenous function of degree 6 c. Homogenous function of degree 4 d. Homogenous function of degree 0 5. Classify the following differential equation: x2dx 2 + dy y = y5dy − xdy − ydx a. Non-linear, homogenous, non-exact b. Linear, homogenous, non-exact c. Non-linear, non-homogenous, non- exact d. Non-linear, non-homogenous, exact 6. Determine the general solution y′ = x − y a. y = x + Ce−x b. y = xex + C c. y = x − 1 + Ce−x d. y = xex − ex + C 7. Determine the general solution √x − x dy dx = y a. y = 2 √ x 3 + C x b. y = − 2 √x 3 + C x c. y = 1 2 √ x3 + C x d. y = − 1 2 √ x3 + C x 8. Which of the following differential equations are exact and homogenous: a. (y3 + x3)dx + 3x2ydy = 0 b. (y2 + x2)dx + xy2dy = 0 c. (y3 + 6x3)dx + 3xy2dy = 0 d. (6x3 + y)dx + (3x)dy = 0 (PART II ON THE NEXT PAGE)