Differential equation with constant coefficients and degree of higher order derivative equal to one is called Linear differential equation. We can solve the linear differential equation with constant coefficient by breaking its solution into two parts. First part is called the complementary function and the second part is called the particular function. Before learning the higher order differential equation, please learn the first order linear differential equation first because it will make you easier to learn the next concepts.

Also, you can check our basic mathematics course before proceeding to the higher engineering maths tutorials for better understanding of the topics. We have also made the gate tutorials to help the students having difficulties in the mathematics syllabus of gate examination.

## Complementary Function (C.F) of Linear Differential Equation

Complementary function (C.F) is the first part of the solution of the linear differential equation with constant coefficients. We can write the equation as F(D)*y = Q, where Q is the function of X. If we assume the value of Q to be zero, then the solution obtained is called the complementary function. The solution can be written as Y = C.F + P.I, Where C.F is the

## Example of Complementary Function

We have included one example problem on finding the complementary function of the linear differential equation with constant coefficients to make the topic more clear. Watch the video tutorial to understand the example’s solution. Before watching this video, make sure that you have already watched the theory explained in the previous video.

## Particular Integral (P.I) of Linear Differential Equation

The complete solution of the differential equation can be expressed as Y = C.F + P.I. We have already discussed finding the complementary function and in this section, we will learn to find the particular integral. If you have not watched the previous videos on this topic, please watch them before proceeding to the next video because every next topic is connected to previous videos. The method to find the P.I varies according to the values of Q. We will discuss a number of cases and their method of solution. Watch the video tutorial to learn about finding the particular integral.

## Cauchy’s Homogenous Equation Reducible to Linear Differential Equation with Constant Coefficients

We can solve the Cauchy’s homogenous linear differential equation by reducing it to constant coefficients form. In the next video tutorial, we will teach you to solve Cauchy’s equation by reducing it to constant coefficients equation.

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