Thread: general solution to DE

dy/dx +2y/x = 4x

find general solution

dy/dx= 4x + x/2y

2y dy = 4x + x dx

2y dy = 5x dx

integrate

y^2 = 2.5 x^2 + C

Originally Posted by harveyo

dy/dx +2y/x = 4x

find general solution

dy/dx= 4x + x/2y

2y dy = 4x + x dx

2y dy = 5x dx

integrate

y^2 = 2.5 x^2 + C

What you have done is not correct.

Your DE is not separable, you need to use the integrating factor method.

Do you know this method?

Read this http://www.mathhelpforum.com/math-he...equations.html

y' + 1/x 2y = 4x

so I(x) = e intergral 1/x dx = e ln x = x

now

x y' + 2y = 4x^2

Originally Posted by harveyo

y' + 1/x 2y = 4x

so I(x) = e intergral 1/x dx = e ln x = x

now

x y' + 2y = 4x^2

make it

now find

= e ln x^2 = x^2 ???

now

x^2 dy/dx + 2/x ^2 y = 4x^3

(x^2 y )' = 4x^3

y = x^2

Originally Posted by harveyo

= e ln x^2 = x^2 ???

now

Yep, great work, now multipling through the whole equation you get



and



by the product rule



Now can you take it from here?