Non exact differential equation, initial value problem

Click For Summary
The discussion focuses on solving the non-exact differential equation y''' - 9y' = 54x - 9 - 20e^(2x) with initial conditions y(0) = 8, y'(0) = 5, and y''(0) = 38. The correct solution is identified as y = 2 + 2e^(3x) + 2e^(-3x) - 3x^2 + x + 2e^(2x). The main issue highlighted is an error in calculating the derivative y', specifically missing the constant term from the derivative of x. This oversight affected the coefficients C2 and C3 in the solution. The discussion emphasizes the importance of careful differentiation in solving initial value problems.
Cocoleia
Messages
293
Reaction score
4

Homework Statement


I am trying to solve the following:
y'''-9y'=54x-9-20e^2x with y(0)=8, y'(0)=5, y''(0)=38

Homework Equations

The Attempt at a Solution


upload_2016-12-8_9-34-25.png

upload_2016-12-8_9-34-52.png


The right answer is:
y= 2+2e^3x+2e^(-3x)-3x^2+x+2e^2x

I am only wrong on the coefficients C2 and C3. Where did I mess up in my solution?
 
Physics news on Phys.org
When computing ##y'## at the top of the second you are missing the constant ##1## coming from ##(x)'##=1.
 

Thread 'Distance between a Clock's hands when the distance is increasing most rapidly'

Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?
View full post »

Similar threads

Question on Two Differentiation Techniques
  • · Replies 25 ·
Replies
25
Views
2K
Solving for the Green's Function and Using It to Solve an Differential Equation
  • · Replies 9 ·
Replies
9
Views
2K
Solve the system of differential equations
  • · Replies 10 ·
Replies
10
Views
2K
Use Wronskian method in solving the given second order differential equation
  • · Replies 7 ·
Replies
7
Views
2K
Another max value on surface (no boundaries)
  • · Replies 8 ·
Replies
8
Views
2K
Reduction of order for Second Order Differential Equation
  • · Replies 2 ·
Replies
2
Views
1K
Solve the initial value problem
  • · Replies 1 ·
Replies
1
Views
1K
Show that the graph is convex for all values of ##x##
  • · Replies 5 ·
Replies
5
Views
2K
Solve Initial Value Problem and Determining Interval
  • · Replies 1 ·
Replies
1
Views
3K
Solving an Euler differential equation
  • · Replies 6 ·
Replies
6
Views
2K