← GATE Mathematics guide GATE Mathematics · Section 5
Ordinary Differential Equations
First- and higher-order ODEs, Laplace & series solutions, Sturm–Liouville and stability — directly covered.
Books that cover Section 5
Looking for the right book for this section? These are the titles from our M.Sc range that cover it — tap through for full contents, price and buy options.
Advanced Ordinary Differential Equations
M.A. & M.Sc. Mathematics · Dr. H.K. Pathak
Covers: The core of the section — existence & uniqueness, higher-order & variable-coefficient linear ODEs, Cauchy–Euler, Laplace transforms, series/Frobenius solutions, Sturm–Liouville problems and systems.
View details 
Special Functions
M.A. & M.Sc. Mathematics · Dr. G.S. Sao
Covers: The Legendre and Bessel functions and their orthogonal properties called out in this section.
View details Full syllabus — Section 5
- First-order ODEs; existence & uniqueness for initial value problems; higher-order linear ODEs with constant coefficients
- Second-order linear ODEs with variable coefficients; Cauchy–Euler equation
- Laplace transforms and their applications to ODEs; series solutions (power series, Frobenius method)
- Legendre and Bessel functions and their orthogonal properties
- Systems of first-order linear ODEs; Sturm oscillation & separation theorems; Sturm–Liouville eigenvalue problems; planar autonomous systems and stability (linearized stability, Lyapunov functions)