You are here:

# Differential Equations/ordinary differential equation

Question
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

Volunteer

#### 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