Differential Equations and Numerical Solutions

MMT-007 important topics

The eGyanKosh units IGNOU has examined most, from 8 past papers. Matched automatically from question wording.

1. Block 3, Unit 9: Multistep and Predictor-Corrector Methods for Solving Initial Value Problems ↗Asked almost every time: in 6 of 8 papers
2. Block 3, Unit 10: Second Order Boundary Value Problems ↗Asked often: in 5 of 8 papers
3. Block 1, Unit 2: Power Series Solutions ↗Asked often: in 5 of 8 papers
4. Block 2, Unit 6: Laplace Transform Method ↗Asked often: in 5 of 8 papers
5. Block 1, Unit 5: Green's Function Method ↗Asked often: in 4 of 8 papers
6. Block 3, Unit 8: Singlestep Methods for Solving Initial Value Problems ↗Asked often: in 4 of 8 papers
7. Block 1, Unit 3: Legendre, Hermite and Laguerre Polynomials ↗Asked often: in 3 of 8 papers
8. Block 2, Unit 7: Fourier Transform Method ↗Asked sometimes: in 2 of 8 papers

MMT-007 assignment

The latest MMT-007 assignment is valid for the January 2026 & July 2026 sessions. It carries 100 marks and 30% of your final grade. Due 31 Mar 2026 for the January 2026 session or 30 Sept 2026 for the July 2026 session.

MMT-007 previous-year question papers

Official term-end exam papers for Differential Equations and Numerical Solutions, published by IGNOU. Each one opens on IGNOU’s website.

• June 2024MMT-007 term-end exam, official PDF↗
• December 2023MMT-007 term-end exam, official PDF↗
• June 2023MMT-007 term-end exam, official PDF↗
• December 2022MMT-007 term-end exam, official PDF↗
• June 2022MMT-007 term-end exam, official PDF↗
• December 2021MMT-007 term-end exam, official PDF↗
• June 2021MMT-007 term-end exam, official PDF↗
• December 2020MMT-007 term-end exam, official PDF↗

Important Differential Equations and Numerical Solutions questions

3 questions have come in more than one MMT-007 exam. They are listed first. The text is taken from IGNOU’s official papers, so open the paper for figures and exact wording.

1. December 2022 · Q6(a) · 5 marksAsked 2 times

   Using the generating function for Jn (x), prove that Jn–1 (x) + Jn+1 (x) = xn2 Jn (x), for integer values of n.

2. December 2020 · Q3(a) · 6 marksAsked 2 times

   Using the method of variation of parameters, determine the appropriate Green’s function for the boundary value problem () ()0, 0 0yy fx y′′ ′++ = = ()20y =, and express the solution as a definite integral.

3. December 2020 · Q5(b)Asked 2 times

   Using the substitution zx=, reduce the equation: 3 04 yxy y′′ ′++= to Bessel’s equation. Hence find its solution.

4. December 2022 · Q1(e)

   The order of the difference method for hyperbolic equations is O(k2 + h2).

5. December 2021 · Q1(c)

   The second order Runge-Kutta method when applied to IVP y' = –100 y, y (0) = 1 will produce stable results for 0 < h < 1.

6. December 2021 · Q1(e)

   Finite element Galer kin method is a weighted residual method and requires the variational form of the given differential equation.

7. December 2020 · Q3(b) · 4 marks

   Find the appropriate value of ()0.4y for initial-value problem ()2,0 1yx yy′ = −=. using multi-step method ()11 32ii ii hy y ff+− = +− with step length 0.2h =. Compute the starting value using Taylor’s series method (second order) with same step-length.

8. December 2020 · Q7(b) · 7 marks

   Consider a steel plate of size 15 cm × 15 cm. If two of its parallel sides are held at 100°C and the other two parallel sides are held at 0°C, determine the steady state temperature at interior points assuming a grid size of 5 cm × 5 cm. Use f ire-point formula.

Differential Equations and Numerical Solutions study material

IGNOU publishes the full MMT-007 self-learning material free on eGyanKosh: every block and unit on ordinary differential equations, partial differential equations, numerical solutions of ordinary differential equations and numerical solutions of partial differential equtaions.