Posted by anonymous on Tuesday, November 1, 2011 at 9:50am.
solve the following differential equation: (x^2+xy)dy=(xyy^2)dx

university maths  drwls, Tuesday, November 1, 2011 at 11:06am
See if this works:
http://www.math.colostate.edu/~gerhard/M345/CHP/ch2_6.pdf
It does not look like it meets the "exact differential" requirements

university maths  Steve, Tuesday, November 1, 2011 at 12:23pm
Good reference. Try looking at the last example:
Substitute y = xv ⇒ dy = v dx+x dv
(xyy^2)dx  (x^2+xy)dy = 0
(x^2v  x^2v^2)dx  (x^2 + x^2v)(vdx + xdv) = 0
2/x dx + (1+v)/v^2 dv = 0
2lnx + (lnv  1/v) = C
ln(x^2v)  1.v = C
vx^2 = Cexp(1/v)
y = vx
xy = Ce^{x/y}
Check my math, as always.

university math  drwls, Tuesday, November 1, 2011 at 10:04pm
I want to congratulate and thank Steve for that very impressive solution.
Answer This Question
Related Questions
 maths  Solve the following differential equation: (1 + x)*(dy/dx) = y where y ...
 maths  Solve the following differential equation: (1 + x)*(dy/dx) = y where y ...
 PLEEEEEAAAASE HELP WITH DIFFERENTIAL EQ PROBLEMS!!  1) What are the equilibrium...
 maths(Differential Equation)  Solve the differential equation below (Y + y^3/3...
 Differential Equations  Solve the seperable differential equation for U. du/dt...
 maths  how would i solve the differential equation dx/dt=kx^2 i.e. solve for x...
 Calculus  Solve the differential equation dy/dx = xe^y and determine the ...
 maths  Solve the following 2nd order differential equation explicitly by ...
 maths  Solve the following 2nd order differential equation explicitly by ...
 Maths  Please help me solve this differential equation: dy/dx(1+1/x)y=y^2
More Related Questions