# university maths

posted by .

solve the following differential equation: (x^2+xy)dy=(xy-y^2)dx

• university maths -

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 -

Good reference. Try looking at the last example:

Substitute y = xv ⇒ dy = v dx+x dv

(xy-y^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 = Cex/y

Check my math, as always.

• university math -

I want to congratulate and thank Steve for that very impressive solution.

## Similar Questions

1. ### maths

how would i solve the differential equation dx/dt=-kx^2 i.e. solve for x as a function of t. I've been told to rearrange the equation to yield dx/x^2=-k dt but what can and should I do now?
2. ### Differential Equations

Solve the seperable differential equation for U. du/dt = e^(5u+7t) - Using the following initial condition U(0) = 12
3. ### maths

Solve the following differential equation: (1 + x)*(dy/dx) = y where y is a funtion of X solve by the following: A)series expansion B) elemantary method please show working
4. ### maths

Solve the following 2nd order differential equation explicitly by expanding up to order x5, y''(x) = (1 + x^2)*y(x) pls show working y =f(x)
5. ### maths

Solve the following differential equation: (1 + x)*(dy/dx) = y where y is a funtion of X solve by the following: A)series expansion B) elemantary method please show working
6. ### maths

Solve the following 2nd order differential equation explicitly by expanding up to order x5, y''(x) = (1 + x^2)*y(x) pls show working y =f(x)
7. ### Calculus

Solve the differential equation dy/dx = -xe^y and determine the equation of the curve through P(1,2) I tried solving the differential equation and I get y = log(x^2/2 + C). Is this correct?