Intro to Differential Equations Problem #1

JosephK
Messages
38
Reaction score
2

Homework Statement


1. Find the general solution to the differential equation:
y''-5y'+6y = 0


Homework Equations





The Attempt at a Solution


m^2 - 5m + 6 = 0
(m-1)(m-5) = 0
y' = Ae^x+Be^5x
 
Physics news on Phys.org
JosephK said:

Homework Statement


1. Find the general solution to the differential equation:
y''-5y'+6y = 0


Homework Equations





The Attempt at a Solution


m^2 - 5m + 6 = 0
(m-1)(m-5) = 0
Your factorization is incorrect. (m - 1)(m - 5) = m2 - 6m + 5, not m2 - 5m + 6.
JosephK said:
y' = Ae^x+Be^5x
 
This cannot be factored.
 
JosephK said:
This cannot be factored.
(m - 3)(m - 2) ?
 
So the answer to this differential equation is

y = c1e^3x+c2e^2x?
 
Yes, and you can check for yourself that your solution satisfies the differential equation. It's always a good idea to check.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

Solve the given differential equation
Replies
4
Views
2K
Given unit impulse response, obtain differential equation
Replies
7
Views
1K
Why can't a critical point of a system of DEs be complex?
Replies
27
Views
2K
How do we write a sinusoidal solution to a 2nd order DE as a sum of exponentials raised to complex roots?
Replies
2
Views
2K
Finding the differential equation of motion
Replies
4
Views
2K
Show that the system of equations has no unique solution
Replies
2
Views
874
Use Wronskian method in solving the given second order differential equation
Replies
7
Views
2K
Verify Green's Theorem in the given problem
Replies
10
Views
2K
Finding the rate of change of x in the equation
Replies
8
Views
1K
Verify Green's Formula for a Simple DE
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top