📚 FYUG (NEP) previous year question papers solution

ASSAM UNIVERSITY, SILCHAR

FYUG 1st semester Physics DSC 101 Previous Year Question Papers Solutions

UNIT 2

Order and Degrees of a differential equation. First Order ODE: General form of first order ODEMdx Ndy   0 , Separation of variables, Exact equation, in-exact equations and integrating factors, Linear equations. Second Order ODE: Homogeneous Equations with constant coefficients. Wronskian and general solution. Complementary function. Methods for finding particular integrals.

2024

(FYUG PHY-DSC101 )

1. Define order and degree of a differential equation.

2. What do you mean by ordinary differential equation (ODE)? Give an example of ODE.

3. When is a differential equation of the form Mdx+ Ndy = 0 said to be exact or inexact

4. Solve the differential equation
(x2 + y2)dx + 2xy dy = 0

5. Solve the differential equation
dy dx + 2xy = 2e−x2

6. What is auxiliary equation? If m1 and m2 are the two roots of the auxiliary equation, then write the expression of complementary function for the cases
m1 = m2
and
m1 ≠ m2

7. Find the solution of the differential equation
d2y dx2 + 4 dy dx + 4y = x2
when
y(0) = 0
y′(0) = 1 2

2024

(FYUG PHY-DSC101 )

8. What is meant by differential equation ? How many types of differential equations are there?

9. Find the order and degree of the differential equation
( d2y dx2 ) 2/3 = ( y + dy dx ) 1/2

10. What are meant by exact and in-exact equations?

11. Solve the differential equation
(4x3 + 6xy + y2) dx dy = −(3x2 + 2xy + 2)

12. Solve the differential equation
dy dx + xy = 2x

13. What is Wronskian? Show that ex and e2x are the linearly independent solutions of
y'' − 3y' + 2y = 0
Find the general solution with conditions
y(0) = 0
y'(0) = 1

14. Solve
y'' − 5y' + 6y = 0


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