Linear Differential Equations Problem no 1 - Differential Equations - Diploma Maths II

TL;DR

This video discusses how to identify and find the integrating factor for linear differential equations using an example.

Transcript

click the bell icon to get latest videos from equator hello friends in this video we are going to see problems which are based on linear differential equation let us start with problem number one in the earlier videos we have seen variable separable method variable separable method using substitution and also homogeneous differential equations now ... Read More

Key Insights

• ✊ Linear differential equations have the power of dy by DX and the value of Y equal to 1.
• 💁 Two basic forms of linear differential equations involve the coefficients P and Q being functions of X or Y.
• 🤨 The integrating factor for linear differential equations is given by e raise to integral PDX.
• 🧑‍🏭 The given example problem requires finding the integrating factor, not the solution to the equation.

Questions & Answers

Q: What are the two basic forms of linear differential equations?

The two basic forms are dy by DX plus py is equal to Q, where the power of dy by DX is 1, and DX by dy plus px is equal to Q, where the power of X is 1. The values of P and Q can be constants or functions of X or Y.

Q: How is the integrating factor for linear differential equations determined?

The integrating factor is found using the formula e raise to integral PDX, where P is the coefficient of Y in the given equation. The integral is taken with respect to X.

Q: What is the integrating factor for the example problem given in the video?

In the example problem, the integrating factor is e^integral of tan(X)DX. Since the integral of tan(X) is log |sec(X)|, the integrating factor simplifies to e^(log |sec(X)|), which is equal to sec(X).

Q: Does the example problem ask to find a solution to the linear differential equation?

No, the question only asks to find the integrating factor. The solution to the differential equation is not required.

Summary & Key Takeaways

• The video explains that linear differential equations have the power of dy by DX and the value of Y equal to 1.

• The example problem asks to find the integrating factor for dy by DX plus y tan X equal to sine 2x.

• The video shows the steps to determine the values of P and Q, and then how to find the integrating factor using the formula e raise to integral PDX.