Differential Equations

Importance

Differential equation is a small topic but has a much larger application in higher mathematics, hence having a topic of great importance. Lets glance over the type of questions asked in exams.

Yearly trend

There is surely one question in both JEE-Advanced and JEE-Mains from differential equations. And since the topic an easy one, grab the chance to take lead from others. Let us look over some ways of solving them.

Topics

The order of a D.E. is the highest ordered differetial appearing in D.E. and its degree is the highest order derivate provided.

Methods of solving D.E.:
1. Variable seperable: Move all variables of one same type on one side and the second on the other, and then integrate both the sides.

  1. Homogeneous Equation(!!dy/dx=f(x,y)!!): Substitute y=kx and resolve further.

  2. Substitution(!!dy/dx=f(ax+by)!!): Let ax+by=t

Then comes the most important and common L.D.E. i.e. Linear Differential Equation. If the equation is !!dy/dx+P(x)y=Q(x)!!, then its solution is given by

!!I.F. (y)=intQ(x).(I.F.)!! where Integrating factor(I.F.) is given by !!e^(intP(x)dx)!!.

The questions are mostly asked amongst this, hence studying just these few concepts can grab off full marks very easily. So don't miss the chance and let us have a practice on the same.

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