PDEs | Proveiff Study

Prove that the Steady state solution of heat equation is unique

By SK Math Expert June 1, 2021PDEsSteady states

Introduction : Here we shall Prove that the Steady state solution of heat equation is unique. Question : Given heat equation \[u_t=u_{xx}\ \ ,\ 0<x<1,\ t>0 \] \[\ u\left(0,t\right)=0\ ,\…

Complementary function and Particular integral of pde

By SK Math Expert May 4, 2021PDEsHomogeneous pde

Introduction: In this solution, we find Complementary function and Particular integral of a pde which is homogeneous and linear Question: find Complementary function and Particular integral of a homogeneous linear…

Particular Integral of linear homogeneous pde

By SK Math Expert May 4, 2021PDEsHomogeneous pde

Introduction: In this solution, we find Particular Integral of homogeneous linear pde Question: Find general solution of linear homogeneous pde \[r+s-2t=0\] Solution:

Homogeneous pde example solved

By SK Math Expert May 4, 2021PDEsHomogeneous pde

Introduction: In this question, we solved homogeneous pde example. Question : Solve Homogeneous pde \[r+2s+t=0\] Solution:

Solved pde 2r+5s+2t=0

By SK Math Expert May 4, 2021PDEshomogeneous pdes

Introduction: In this solution, we find complementary function of pde 2r+5s+2t=0. Question: solved pde \[2r+5s+2t=0\] Solution:

Homogeneous linear partial differential equation solution example 2

By SK Math Expert April 24, 2021PDEsHomogeneous linear partial differential equation

Introduction: in this question, we find solution of a Homogeneous linear partial differential equation solution example 2. Its step by step explanation is as follows Question : solve Homogeneous linear…

Homogeneous linear pde solution example 1

By SK Math Expert April 24, 2021PDEsHomogeneous linear partial differential equation

Introduction: In this question, we explain how to solve Homogeneous linear pde solution example 1. Question: Solve Homogeneous linear pde Solution: First we know the method that we shall use…

How to solve pde ut+aux=e^(-2x), u(x,0)=f(x)

By SK Math Expert February 26, 2021Advanced Math, PDEssolutions of first order pdes

Introduction : In this solution we explain step by step the method How to solve pde ut+aux=e^(-2x), u(x,0)=f(x). Question: solve pde \[u_{t}+au_{x}=e^{-2x}\] subject to initial condition \[u(x,0)=f(x)\] Solution: Given pde…

Hyperbolic partial differential equation Example 1

By SK Math Expert July 19, 2020PDEsclassification of pdes, hyperbolic pde, pde

Introduction : The question "prove that a partial differential equation is hyperbolic" is asked in many competitive exams. In this article, we will learn all the steps by solving an…