Math by Tathagata
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). Study Material: (more will follow soon) Ordinary Differential Equation (ODE) Problems Q1: Find the order and degree of $\left(\dfrac{d^3y}{dx^3} \right)^5+x^2y \left( \dfrac{d^4y}{dx^4} \right)^2=\sin(\ln x)$. Q2: Find the value of $m$ … 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