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solve the differential equation :

2xydy = 5dy - dx

2xydy = 5dy - dx ==> dy/dx = 1/(5-2xy) ==> dx/dy = 5-2xy, which is a 1st order linear ODE

for x as a function of y.

==> dx/dy + 2yx = 5, integrating factor is u(y)=e^integral(2y dy)=e^(y^2)

==> [x e^(y^2)]' = 5e^(y^2), where the prime means differentiate w.r.t. y

==> x e^(y^2) = 5*integral(e^(y^2) dy) + C

==> x = e^(-y^2)[5*integral(e^(y^2) dy) + C]

Differential Equations

Answers by Expert:

Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!

Over 15 years teaching at the college level.**Organizations**

NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.**Education/Credentials**

B.S. in Mathematics from Rensselaer Polytechnic Institute

M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook