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Differential Equations/ordinary differential equation

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Question
solve the differential equation :
2xydy = 5dy - dx

Answer
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

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Abe Mantell

Expertise

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!

Experience

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

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