Math by Tathagata
Cauchy-Euler equation (or Cauchy’s linear equation) is a differential equation with non-constant coefficients i.e, having variable-coefficients. It has the following form where a0, a1, …, an are real constants, and f(x) is a function of x. How to Solve Cauchy-Euler Equation? The below steps to be followed in order to solve a Cauchy-Euler equation. Solved … Read more
In this page, lets explore the variation of parameters method for solving a second order differential equation with examples. Variation of Parameters Formula Formula: Let u and v be two linearly independent solutions of y”+py’+qy=0. Then the general solution of y”+py’+qy=R obtained by using the method of variations of parameters is given by $y=u \displaystyle\int … Read more
Form ODE by Eliminating a and b: In this article, let’s learn how to form an ordinary differential equation (ODE) by eliminating a and b which are arbitrary constants. Lets solve some problems. Solved Problems $\boxed{\color{blue}\textbf{Q}1:}$ Eliminate the arbitrary constants a, b and c to from an ordinary differential equation. $\boxed{\color{red}\textbf{Answer:}}$ Part (1) Given y … Read more
An orthogonal trajectory is a curve that intersects another family of curves at right angles. In this post, we study orthogonal trajectory along with a few questions and answers. Definition of Orthogonal Trajectory An orthogonal trajectory of a family of curves is a curve that intersects every member of that family at a right angle. … Read more
This is the page for Differential Equation practice problems. Here, a list of practice problems will be given for the course on Differential Equation (Exercise). Final Sem Practice Problems The set of practice problems is divided into two parts: Ordinary Differential Equation and Partial Differential Equation. Ordinary Differential Equation Problems Q1: Eliminate A and B … Read more
The particular integral of a differential equation is needed to find to solve the equation. In this article, lets learn how to find particular integral with formula and method. Method of Finding Particular Integral (PI) Let us consider a second order linear differential equation with constant coefficients: $\dfrac{d^2y}{dx^2}+a\dfrac{dy}{dx}+by=Q(x)$ …(1) where a and b constants and … Read more
The general form of linear differential equation of first order is of the form: dy/dx + P(x)y = Q(x) where P(x) and Q(x) are functions of x. Using integrating factor method, we solve this equation. In this article, let us learn how to solve a first order linear differential equation with examples. Integrating Factor of … Read more