Can You Help Solve These Complex Mathematical Equations?

[ferry2]

Hi, friends .

These are two equations, which were unable to resolve. Hope to help me. Note: this is not home, I just want to see how to resolve the equations. Thank answered.

$$(2y-x+1)dx-(x-3y^2)dy=0$$

Find the common solution of the Euler's eqution:

$$(2x+1)^2y''-2(2x+1)y'+4y=0,$$ $$x>-\frac{1}{2}$$

 

[ross_tang]

Hello ferry2, I have solved your 2nd equation here:

http://www.voofie.com/content/146/how-to-solve-2x12-y--2-2x1-y-4-y-0/"

And the solution is given by:

$$y(x) = C_1(2x+1) +C_2 (2x+1) \ln (2x+1)$$

 

[ferry2]

Thanks a lot Ross Tang! Can you tell something about first equation?

 

[ross_tang]

I tried various method in solving the 1st equation, but without any success. Sorry.

 

[JJacquelin]

Hello !

May be a typo in the 1st equation ? No difficulty if (2x-y+1) instead of (2y-x+1).
2nd equation : Let t=ln(2x+1) leads to
d²y/dt² -dy/dt +y =0
y(t) = exp(t)*(a*t+b)
and y(x) according to ross_tang formula.

 

[ferry2]

It is possible there have been a typo. Thank you both.