Answer to Question #343407 in Differential Equations for Themba

Question #343407

(x^3+y^3)=(3xy^2)dy/dx


1
Expert's answer
2022-05-23T23:18:42-0400

A Bernoulli differential equation


"\\dfrac{dy}{dx}-\\dfrac{1}{3x}y=\\dfrac{x^2}{3}y^{-2}"

Substitute

"z=y^{1-(-2)}=y^3"

"\\dfrac{dz}{dx}=3y^2\\dfrac{dy}{dx}"

"\\dfrac{dy}{dx}=\\dfrac{1}{3y^2}\\dfrac{dz}{dx}"

Then


"\\dfrac{dz}{dx}-\\dfrac{1}{x}z=x^2"

"IF=e^{\\int (-1\/x)dx}=\\dfrac{1}{x}"

"\\dfrac{1}{x}\\dfrac{dz}{dx}-\\dfrac{1}{x^2}z=x"


"\\dfrac{d}{dx}(\\dfrac{z}{x})=x"

"\\dfrac{z}{x}=\\dfrac{x^2}{2}+C"

"z=\\dfrac{x^3}{2}+Cx"

"y^3=\\dfrac{x^3}{2}+Cx"


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS