Higher Order Linear Differential Equations — Study Resources & PYQs
Solution of higher-order linear ordinary differential equations.
- Estimated study time: 30 minutes
Study resources
- Differential Equation playlist contents - GP Sir (Class Central index) (Article) — Indexed list of a 23-hour lecture series. Look for 'Linear Higher Order Differential Equation | CF & PI' Lecture I, which introduces this topic.
- Paul's Online Math Notes - Differential Equations (full index) (Article) — Master index of the whole DE course: second order and higher order equations, undetermined coefficients, variation of parameters, Euler equations and Fourier series. Bookmark this one link.
- Wikipedia - Linear differential equation (Article) — Section on higher-order linear equations with constant coefficients, the auxiliary/characteristic equation, and the structure of the general solution.
- Series Solution of Differential Equations - Dr. Gajendra Purohit (GP Sir), curated by Class Central (Video) — 7-hour video series that, alongside series solutions, works through solving higher-order linear differential equations and finding their complementary function and particular integral.
- Wikipedia - Laplace transform applied to differential equations (Article) — Study resource for Higher Order Linear Differential Equations.
- Ordinary Differential Equation 2.0 (Updated Lectures) - GP Sir (Video) — Latest ODE series starting from order and degree, then variable separable, homogeneous, linear and Bernoulli forms. This is the recommended playlist for the ODE part of the syllabus.
- Paul's Online Math Notes - First Order Differential Equations (Article) — Paul's Online Math Notes - First Order Differential Equations — selected for the syllabus topic Higher Order Linear Differential Equations.
Higher Order Linear Differential Equations previous year questions
- Solve the following partial differential equations: (a) $(D^2 + 2DD' + D'^2)z = x^2 y$ (b) $(D^2 + D'^2 + 2DD' - 1)z = 5e^x \cos y$
- a) Draw the graph of the function $$f(x) = \begin{cases} 0, & -\pi \le x \le 0 \\ x^2, & 0 < x \le \pi \end{cases}$$ Is it even or odd? Also expand it as a Fou…
- Using power series method, solve the legendre's differential equation of order 3.
- Find two power series solution of Bessel's differential equation of order $1/2$.
Taught in these subjects
- ENGINEERING MATHEMATICS-II — BMAT21 · Government College of Engineering and Technology, Jammu
- ENGINEERING MATHEMATICS-II — BMAT21 · Government College of Engineering and Technology, Jammu
- Engineering Mathematics-II — BMAT21 · Government College of Engineering and Technology, Jammu
- Engineering Mathematics-II — BST1201 · Government College of Engineering and Technology, Jammu
- Engineering Mathematics-II — BST1201 · Government College of Engineering and Technology, Jammu