differential equation & linear algebra equation.
I need to know how to use Bernoulli Equation to solve for xy' + y + x^2y^2e^x

Question

differential equation & linear algebra equation.
I need to know how to use Bernoulli Equation to solve for xy' + y + x^2y^2e^x

adunb8 · Answer

i want to know the step by step.

anonymous · Answer

$$xy'+y=x^2e^xy^2$$

adunb8 · Answer

uh... step by steps?

anonymous · Answer

adunb8 · Answer

.... okay thanks

lgbasallote · Answer

lol..wikipedia

adunb8 · Answer

oh! can you help?!

lgbasallote · Answer

i'll let @mukushla do his thing

adunb8 · Answer

....

adunb8 · Answer

his using wikipedia...

anonymous · Answer

$$z'=-\frac{y'}{y^2}$$$$xy'+y=x^2e^xy^2$$divide by y^2$$x\frac{y'}{y^2}+\frac{1}{y}=x^2e^x$$now u have$$-xz'+z=x^2e^x$$

anonymous · Answer

this is a first order linear diff equation solve it for z

adunb8 · Answer

okay thank you for the help ~.~

anonymous · Answer

welcome

lgbasallote · Answer

do you know the form of Bernoulli's equation @adunb8 ?

adunb8 · Answer

well know i looked at it it looks like its $$y' + p(x)y = q(x)y^n$$

lgbasallote · Answer

right

lgbasallote · Answer

so your first step should be to transform your equation into that form

adunb8 · Answer

yes i made it into $$y' + x^{-1} y = xy^2e^x$$

lgbasallote · Answer

wait....what's the original equation?

adunb8 · Answer

$$xy' + y + x ^{2}y ^{2}e ^{x}$$

adunb8 · Answer

= 0