**Maths Differential Equation **

**Solved Practice Sample Paper on JEE Advanced Pattern**

Sub-Topic of Maths Differential Equation

Partial differential equation :(a) Nonlinear partial differential equation (b) list of nonlinear partial differential equationsBoundary conditionBoundary value problem :(a) Dirichlet problem, Dirichlet boundary condition (b) Neumann boundary condition (c) Stefan problem (d) Wiener–Hopf problemSeparation of variablesGreen’s functionElliptic partial differential equationSingular perturbationCauchy–Kovalevskaya theoremH-principleAtiyah–Singer index theoremBäcklund transformViscosity solutionWeak solution

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## 01. JEE Advanced Maths Differential Equation

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## 01. JEE Advanced Maths Differential Equation

Paper01Download## JEE Advanced Maths Differential Equation Solution

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First Order Maths Differential Equations

Linear EquationsIdentifying and solving linear first order differential equations.

Separable EquationsIdentifying and solving separable first order differential equations. We’ll also start looking at finding the interval of validity from the solution to a differential equation.Exact Equations Identifying and solving exact differential equations. We’ll do a few more interval of validity problems here as well.

Bernoulli Differential EquationsIn this section we’ll see how to solve the Bernoulli Differential Equation. This section will also introduce the idea of using a substitution to help us solve maths differential equations.

SubstitutionsWe’ll pick up where the last section left off and take a look at a couple of other substitutions that can be used to solve some differential equations that we couldn’t otherwise solve.

Second Order Maths Differential Equations

Basic ConceptsSome of the basic concepts and ideas that are involved in solving second order differential equations.

Real RootsSolving differential equations whose characteristic equation has real roots.

Complex RootsSolving maths differential equations whose characteristic equation complex real roots.

Repeated RootsSolving differential equations whose characteristic equation has repeated roots.

Reduction of OrderA brief look at the topic of reduction of order. This will be one of the few times in this chapter that non-constant coefficient differential equation will be looked at.

Laplace Transforms

The DefinitionThe definition of the Laplace transform. We will also compute a couple Laplace transforms using the definition.

Laplace TransformsAs the previous section will demonstrate, computing Laplace transforms directly from the definition can be a fairly painful process. In this section we introduce the way we usually compute Laplace transforms.

Inverse Laplace TransformsIn this section we ask the opposite question. Here’s a Laplace transform, what function did we originally have?

Dirac Delta FunctionOne last function that often shows up in Laplace transform problems.

Convolution IntegralA brief introduction to the convolution integral and an application for Laplace transforms.Table of Laplace Transforms This is a small table of Laplace Transforms that we’ll be using here.

Higher Order Maths Differential Equations

Basic Concepts for nth OrderLinear Equations We’ll start the chapter off with a quick look at some of the basic ideas behind solving higher order linear differential equations.

Linear Homogeneous Differential EquationsIn this section we’ll take a look at extending the ideas behind solving 2nd order maths differential equations to higher order.

Undetermined CoefficientsHere we’ll look at undetermined coefficients for higher order differential equations.

Boundary Value Problems & Fourier Series

Boundary Value ProblemsIn this section we’ll define the boundary value problems as well as work some basic examples.

Eigenvalues and EigenfunctionsHere we’ll take a look at the eigenvalues and eigenfunctions for boundary value problems.

Periodic Functions and Orthogonal FunctionsWe’ll take a look at periodic functions and orthogonal functions in section.

Partial Maths Differential Equations

The Heat EquationWe do a partial derivation of the heat equation in this section as well as a discussion of possible boundary values.

The Wave EquationHere we do a partial derivation of the wave equation.

TerminologyIn this section we take a quick look at some of the terminology used in the method of separation of variables.

Laplace’s EquationWe discuss solving Laplace’s equation on both a rectangle and a disk in this section.

**How to write in a straight line without lined paper?**

I can not write in a straight line unless. I have lined papers to help guide me along the pages. However some-times the task calls for plain-paper where no such lines are in place *(i.e. a poster or some such)*.

I usually write with a ball point pen. However, in the case of a poster, I use felt tip pen which is more susceptible to smudging if rubbed too much / too soon!

*How can I make sure that I am writing in a straight line without using lined paper?*

*How can I make sure that I am writing in a straight line without using lined paper?*

I have tried placing a ruler along the page but this messes up my handwriting and it looks a bit weird so I would rather try a new method.

**There a several options to create an invisible line to help you write:**

- Draw thin lines with a pencil and erase them afterwards. If you work with a soft pencil and without much force, the lines are easily erasable and you won`t mark the sheet.
- If you are working on a poster, you could also provide a line with the help of a beamer/over head projector or some fancy laser liner. It should work best if you are left handed, since you otherwise cover the line with your arm/hand.
- Also, you can work at the edge of a table or by placing a ruler under the paper. You will notice directly if you are not on the line. But it will be not beneficial for your style.