SOLUTION: Solve the initial value problem y'+y/2x=xy^-3,y(1)=2.Please help me.

Question 976251: Solve the initial value problem y'+y/2x=xy^-3,y(1)=2.Please help me.
Answer by t0hierry(194) (Show Source): You can put this solution on YOUR website!
y^3dy + y^4/2xdx = x
u = y/sqrt(x)
y = u sqrt(x)
y' = u' sqrt(x) + u/2sqrt(x) = x/y^3
u'x + u/2 = sqrt(x)^3/y^3 = 1/u^3
xdu = (1/u^3 - u/2)dx
du/(1/u^3 - u/2) = dx/x
du 2u^3/(2-u^4) = dx/x
call v = 2 - u^4
then dv = -4 u^3 du
-2 dv/v = dx/x
integrate
v^(-2) = 1/x + constant
y(1) = 2 means 1 + constant = 2 - 2^4/1 = 2 - 16 = -14
constant = 15
If I didn't make any mistake (please check) then
(2 - y^4/x^2)^(-2) = 1/x + 15

RELATED QUESTIONS
Please help me to solve this problem. Given that (x + y)*2=63 and xy=65, find the value... (answered by josgarithmetic)

Solve the systems a)x^2+y^2=25 3x+y=13 b) xy=20 y=2x-3 c) 2x^2-xy+y^2=11 (answered by lynnlo)

Please help me solve this problem: y=1/2x-3 y=1/3x+2 I tried this y=1/3x+2... (answered by stanbon)

use Runge-Kutta method to solve the initial value problem f(x,y)=1+xsinxy , with h=0.1 ,... (answered by Fombitz)

Please help me solve this problem . Consider the differential equation... (answered by Fombitz)

Please help me solve for x and y simultaneously {{ y-2x+1 and... (answered by Alan3354)

Hello, Please help me solve this problem, thanks in advance. xy=1... (answered by mananth,neatmath)

please help me solve this graphing problem Solve the following system: y = 2x - (answered by jim_thompson5910)