My Math Forum  

Go Back   My Math Forum > College Math Forum > Differential Equations

Differential Equations Ordinary and Partial Differential Equations Math Forum


Reply
 
LinkBack Thread Tools Display Modes
March 23rd, 2016, 04:57 AM   #1
Newbie
 
Joined: Mar 2016
From: london

Posts: 1
Thanks: 0

Particular solution differential equations

Hi there in major help with the questions attached to this.
Need to determine the particular solution of the following differential equations:
3t(t-dy/dt)=7. Given that y=4 when t=2

And

1/e^x + 5= x+5 dy/dx. Given that y=2 when x=0

So stuck with these and don't know what to do.image.jpg
harrypalmer101 is offline  
 
March 23rd, 2016, 05:53 AM   #2
Global Moderator
 
Joined: Dec 2006

Posts: 18,154
Thanks: 1418

The differential equation in the second problem can be integrated immediately by integrating each term. Can you give that a try and post your work?
skipjack is online now  
March 26th, 2016, 05:17 AM   #3
Math Team
 
Joined: Jan 2015
From: Alabama

Posts: 2,822
Thanks: 750

Looks pretty much like basic Calculus. I would start by writing the equation as 3dy/dt= 3t^2- 7 so that, in differential form, 3dy= (3t^2- 7)dt and integrating both sides 3y= t^3- 6t+ C. Since y(2)= 4, 3(4)= 2^3- 6(2)+ C so 12= 8- 12+ C and C= 16. y(t)= (t^3- 6y+16)/3.
Country Boy is offline  
April 26th, 2016, 07:30 AM   #4
Global Moderator
 
Joined: Dec 2006

Posts: 18,154
Thanks: 1418

Quote:
Originally Posted by harrypalmer101 View Post
3t(t-dy/dt)=7. Given that y=4 when t=2
I'll assume that t > 0, then dividing by t gives 3t - 3dy/dt = 7/t.
Integrating gives 3t²/2 - 3y = 7ln(t) + C, where C is a constant.
Substituting t = 2 and y = 4 gives 6 - 12 = 7ln(2) + C, so C = -6 - 7ln(2).
Hence y = t²/2 - (7/3)ln(t/2) + 2.
skipjack is online now  
Reply

  My Math Forum > College Math Forum > Differential Equations

Tags
differential, equations, solution



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
[ASK] Solution of Differential Equations Monox D. I-Fly Differential Equations 10 June 14th, 2015 04:22 AM
Differential Equations: General & Particular Solution aliaja Differential Equations 1 September 17th, 2013 04:31 PM
Differential Equations Verifying Implicit Solution aztakurva Differential Equations 2 August 22nd, 2013 07:15 PM
differential equations solution - help! science Differential Equations 2 July 17th, 2013 09:08 AM
how to find a solution the differential equations mulyak.oleksandr Differential Equations 1 September 5th, 2012 07:17 AM





Copyright © 2017 My Math Forum. All rights reserved.