Abel's Equation and Wronskian for find out y2

  • Thread starter Thread starter maiacaroline
  • Start date Start date
  • Tags Tags
    Ode Wronskian
maiacaroline
Messages
1
Reaction score
1

Homework Statement


x²y''+xy'+(x²-0,25)y=0
y1= x^-1/2*sin x

Homework Equations


Abel's equation:
W= c.e^-(integrate (p(t))

The Attempt at a Solution



My Wronskian gave me a first order ODE that I really don't know solve.

x^-1/2*sinx y' + (1/2 x^-3/2 sin x- x^-1/2cosx) y2

I don't solved the Abel's equation cause I don't know what to do with this amount of sin and cos ahahhahaha.

Is the exercise 37 of Boyce and Diprima
 
  • Like
Likes makemoneyu
Physics news on Phys.org
Since you are given one solution you should use the method of reduction of order to find the other one, and it should be in the chapter where you found the question (did it myself a few months ago).
 

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

Understanding Wronskian of solutions to homoeneous 2nd order linear DE
Replies
2
Views
1K
Variation of parameter VS Undetermined Coefficients
Replies
7
Views
2K
Using Abel's Theorem, find the Wronskian
Replies
1
Views
2K
Finding Wronskian of Diff. Eq. with Abel's Formula: Help Needed
Replies
3
Views
2K
Solve the given differential equation
Replies
3
Views
564
A Wronskian- variation of Params Problem
Replies
1
Views
1K
Wronskian Equation for y1 and y2 with Initial Conditions
Replies
2
Views
1K
How to Show the Wronskian of Three Distinct Solutions Equals Zero?
Replies
19
Views
3K
Finding Wronskian with Given Initial Conditions for Non-Homogeneous ODE
Replies
1
Views
2K
Construct a second order ODE given the solutions?
Replies
11
Views
3K

Hot Threads

Recent Insights

Back
Top