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Differential Equations Past Paper 2019
University: University of Sargodha (UOS)
Program: BS Computer Science – 3rd Term
Subject: Differential Equations (MATH-2215)
Year: 2019
Time Allowed: 2 Hours 30 Minutes
Maximum Marks: 80
University of Sargodha
BS 3rd Term Examination 2019Subject: Computer Science
Paper: Differential Equations (MATH-2215)
Time Allowed: 2:30 Hours
Maximum Marks: 80Note: Objective part is compulsory. Attempt any four questions from subjective part.
Objective Part (Compulsory)
Q.1 Write short answers of the following in 2–3 lines each. (2 × 10)
- Define partial differential equation.
- Define explicit solution.
- Determine whether the DE u dv + (v + uv − v²u) du is linear in u.
- Verify that y = ax + a² is an explicit solution of the DE: 2y′ + y = 0.
- State Newton’s law of cooling and warming and give its mathematical model.
- Find the integrating factor of the linear equation: 3 dy/dx + 12y = 4.
- Write general form of homogeneous linear nth-order differential equation.
- Determine whether the set of functions f₁(x)=x, f₂(x)=x−1, f₃(x)=x+3 is linearly independent.
- Write the auxiliary equation and general solution of y″ − 10y′ + 25y = 0.
- Define separable equation.
Subjective Part (Attempt Any Four)
Q.2 Solve the given IVP using proper substitution.
Q.3 Determine whether the given DE is exact. If exact, solve it.
Q.4 Solve the given differential equation by method of undetermined coefficients.
Q.5 Solve the given system of differential equations by systematic elimination.
Q.6 Find the power series solution of the DE.
Q.7 Use improved Euler’s method to obtain decimal approximation.
Why Use This Differential Equations Past Paper?
This past paper helps students understand exam patterns, practice important concepts, and prepare both objective and subjective questions effectively.
- Practice key definitions and concepts
- Strengthen problem-solving skills
- Understand frequently repeated questions
- Prepare efficiently for university exams
Download Differential Equations Past Paper (PDF)
You can download the official PDF of this paper here:
Download Differential Equations Past Paper 2019 (PDF)
Objective Part – Short Question Solutions
1. Define partial differential equation.
A partial differential equation involves partial derivatives of a function with respect to two or more independent variables.
Reference: Wolfram MathWorld
2. Define explicit solution.
An explicit solution expresses the dependent variable directly in terms of the independent variable.
Reference: Paul’s Online Math Notes
3. Is the given DE linear in u?
The equation is not linear in u because the dependent variable and its derivative are multiplied together.
Reference: Khan Academy
4. Verify explicit solution.
The given function satisfies the differential equation after substitution, hence it is a valid explicit solution.
Reference: Paul’s Notes
5. Newton’s law of cooling.
It states that the rate of change of temperature is proportional to the difference between object temperature and surroundings.
Reference: MathWorld
6. Define integrating factor.
An integrating factor is a function used to convert a non-exact linear DE into an exact equation.
Reference: Paul’s Notes
7. General form of homogeneous linear DE.
It is an equation where all terms involve the dependent variable or its derivatives and equals zero.
Reference: MathWorld
8. Linear independence of functions.
The given functions are linearly independent if no non-trivial linear combination equals zero.
Reference: Khan Academy
9. Auxiliary equation and solution.
The auxiliary equation is obtained by replacing derivatives with powers of m to solve linear DEs.
Reference: GeeksforGeeks
10. Define separable equation.
A separable equation can be written as a product of a function of x and a function of y.
Reference: Paul’s Notes