# What is Particular solution: Definition and 104 Discussions

In mathematics, an ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and the derivatives of those functions. The term ordinary is used in contrast with the term partial differential equation which may be with respect to more than one independent variable.

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37. ### 1st order, nonhomogeneous, linear DE - particular solution

I know nothing about DEs, so this may be a silly question. I'm given some time varying (x_t)_t and a constant r, and I want to solve the equation u_t = rx_t + \dot u_t for u. What I know so far is that (solving the homogeneous equation) if \bar u is some particular solution, then any u is...
38. ### Struggling with ODE: Find Particular Solution y(0)=1

i am having issues solving an ODE it is given as y'= (1-2y-4x)/(1+y+2x) I've been told to find the particular solution when y(0)=1 please help

Did it :)
40. ### Find a particular solution for a non-homogeneous differential equation

Find a particular solution for the following equation: y"+2y'+y=12.5e-t I'm not sure on which method to use. Here's my attempt using the undetermined coefficients method: →y"+2y'+y=12.5e-t r2+2r+1=0 r=-1 *not even sure if this part is useful →yp=e-t yp'=-e-t yp"=e-t...
41. ### Nonhomogeneous system particular solution.

Homework Statement Verify that the vector functions x_{1}=\begin{bmatrix}e^{t}\\ e^{t}\end{bmatrix} and x_{2}=\begin{bmatrix}e^{-t}\\ 3e^{-t}\end{bmatrix} are solutions to the homogeneous system x'=Ax=\begin{bmatrix}2 & -1 \\ 3 & -2 \end{bmatrix} on (-\infty ,\infty ) and that x_{p}...
42. ### Find the particular solution to Dy/Dx = 3x^2 + 1

Find the particular solution to Dy/Dx = 3x^2 + 1 when y(0) = 3 I've looked everywhere for steps to solve this problem, and every website I have been to has taught me how to do a question like this when each side has a Y (is separable) but I can't find out how to do one like the question above...
43. ### Finding the particular solution to the differential equation

Homework Statement Please see attachment Homework Equations Please see attachment The Attempt at a Solution Please see attachment. I am supposed to compare coefficients but it doesn't seem possible. what do I do next? (also, if i have posted this in the wrong forum...I...
44. ### Write the complete solution as the particular solution plus any multip

Homework Statement Could someone please help me do this problem?: “Write the complete solution as x_p plus any multiple of s in the nullspace: x + 3y + 3z = 1 2x + 6y + 9z = 5 –x – 3y + 3z = 5” The answer is x = x_p + x_n = {{-2},{0},{1}} + x_2 {{-3, 1, 0}}. Homework Equations Ax...
45. ### Difference between particular integral and particular solution?

difference between particular integral and particular solution..?? particular integral and particular solution are used to find the solution of differential equation..but sometimes they are used interchangeably but what's the difference between two..?? please state examples..!
46. ### How to make a gel for/of a particular solution?

Hi! I performed the blue bottle experiment using Methylene Blue, water, NaOH and Glucose. The reaction went fine but I have planned to make a gel of the reactants EXCLUDING glucose and then add glucose in controlled amounts to this gel to see the effects. I know it may sound like an...
47. ### Difference between unique solution and particular solution

Homework Statement For 1st order linear ordinary differential equation, how do "unique solution" and "particular solution" differ? Homework Equations if dy/dx = f(x,y) and partial f(x,y) with respect to y are both continuous, then there exists a unique solution within a region R...
48. ### Find the appropriate particular solution.

Homework Statement Find the appropiate particular solution form for y''' - y'' - 12y' = x - 2x*e^-(3x) DO NOT SOLVE FOR THE COEFFICIENTS Homework Equations Just guessing proper solution forms for nonhomogeneous second order D.Es with undetermined coefficients. The Attempt at a Solution...
49. ### Engineering Solve Particular Solution for R3 in Circuit with V1=V2=L1=L2=0

1. Homework Statement The problem says: For the next circuit obtain a particular solution for R3 when v1=v2=l1=l2=0 at t=0. vs= cos(wt) dc source= 10v *R3 is the 1k resistor. http://postimage.org/image/fxtu2blaf/ 2. Homework Equations Kirchoff current law...
50. ### Finding particular solution to differential equations

There are two questions that I am trying to solve on web assignment. The goal is to find a general form of a particular solution to each ODE. The question asks me to represent all constants in the solution using "P,Q,R,S,T..etc.", in that order. 1. y'''-9y''+14y'=x2 2. y''-9y'+14y=x2e4x...