Question

Bernoulli Equation Differential Eqn.
HELP i dont understand..

Answer 1

\[y^2(xy'+y)(1+x^4)^(1/(2)=x \]

Answer 2

isnt bernoulli similar to like a u substitution?

Answer 3

\[y^2(xy'+y)(1+x^4)^{1/2}=x\]
\[y^2(xy'+y)=\frac{x}{\sqrt{1+x^4}}\]
\[y^2xy'+y^3=\frac{x}{\sqrt{1+x^4}}\]
\[y^2y'+\frac{1}{x}y^3=\frac{1}{\sqrt{1+x^4}}\]
\[z=y^3~;~z'=2y^2~y'~;~\frac12z'=y^2y'\]
\[\frac12z'+\frac{1}{x}z=\frac{1}{\sqrt{1+x^4}}\]
\[z'+\frac{2}{x}z=\frac{2}{\sqrt{1+x^4}}\]
solve for z

Answer 4

z' = 3y^2 y' but other than that i think its good :)

Answer 5

tnx!!