Word Count : 632

---

We are asked to solve the differential equation: $$ y' = \frac{zy^4 + x^4}{x y^3}. $$ First, let's clarify the notation. Assuming $z = y'$, the equation becomes: $$ y' = \frac{y' y^4 + x^4}{x y^3}. $$ Multiply both sides by $x y^3$: $$ x y^3 y' = y' y^4 + x^4. $$ Bring terms containing $y'$ to one side: $$ x y^3 y' - y^4 y' = x^4. $$ Factor $y'$ on the left: $$ y'(x y^3 - y^4) = x^4. $$ So we get: $$ y' = \frac{x^4}{x y^3 - y^4} = \frac{x^4}{y^3 (x - y)}. $$ Now we have a separable form: $$ \frac{dy}{dx} = \frac{x^4}{y^3 (x - y)}. $$ Let us try the substitution $v = \frac{y}{x} \implies y = vx \implies _______ ____ ______ _________ ___ ________ ________ ________ __________ _______ ______ ___.
______ _________ ____ __________ ______ ________ ____ _____ _________ ________.
________ ______ ________ _____ __________ __________ ________.
_______ ______ __________ _____ _________ _______.
_________ _____ ___ __________ ______ ______ __________.
____ _______ ________ _________ __________ ______ _______ ____.
___ _________ ___ ____ _____ __________ _________ _______.
__________ ______ ____ ________ ____ _________.
_______ ___ _____ __________ __________ __________ __________ _______.
________ ___ ______ ________ ____ _____ _________.
_______ _____ _______ ___ ____ _______ ___ ________ __________.
_____ __________ ________ _______ ____ ______ __________ ________ ________ ______.
________ _____ ___ ____ _______ ___.
___ __________ ______ ____ _____ ____ ____ _________ ___ _________ __________ _______.
______ ________ ________ _______ __________ _________ __________ __________.
__________ _____ _______ ________ ________ ____ ______.
______ _______ ________ ____ __________ __________.
____ __________ _________ ________ _______ ___ _____ ___ __________ _______ ______ ______.
___ ____ ___ ________ _______ ___ ______ _____ __________ _______ ____ ____.
________ _____ _______ _______ _______ ___ ___ ____.
_________ __________ ______ ________ ________ _______ _____ ______ ____ ________.
________ _____ ________ ______ ____.
_______ _________ _________ ____ _________ ____ ___ __________ _________ ___.
_____ _________ _______ ___ _____ _______ _______ ______.
_______ _________ __________ ______ _____ ________ _________ ______ _________.
_______ ______ ________ _____ _________ _______ ____ _________ ___ _______ ______ ___.
____ ________ __________ ___ _________ _________ __________.
___ ______ ________ ____ _____ _________ ________ ______.
_______ __________ ________ ________ __________ _____.
__________ __________ _______ _______ ________ ___ __________ ____.
__________ ________ _____ ______ ________ _________ _______.
_______ _____ ________ ________ _____ _____ ______ ______ __________ __________ ________ __________.
______ ________ ________ __________ ______ _____.
_____ _____ _____ _______ ___ _______ ______ _________ ___ _________ ________ __________.
___ ______ ______ _____ ___ _________.
_______ ____ _________ ___ _______.
______ ___ _______ _________ _______ ___ _________ _________ __________ _____.
___ ___ _____ _____ ___ _________ _____ ______ _________ _____.
_______ _____ _____ ______ _________ __________ __________ _______ ______.
_______ __________ ____ __________ _______.
__________ _________ ___ _______ ________ ______ ___ _____ _____ _______ ______.
_________ ___ _______ __________ _______.
______ _______ _________ ____ _______ ____ _____ ____.
________ _________ _________ _____ _________ ________.
_______ ___ __________ ____ _____ _______ _______ ___ _____ _______ ___ _________.
____ _______ __________ ______ ___ _____ ________.
____ ______ _________ ____ _______ _____ _____ ____ ______ __________ ___ ________.
_______ __________ ________ __________ _______ _______ ____ __________ __________ ________ _______.
_________ ____ _____ _________ _____.
____ _____ _____ _________ _____ ___ ______ ________ __________ _______ _____.
_______ _________ ______ ___ ____ ___ ___ ___.
______ ___ _________ __________ __________ __________ ________ ______.
___ ____ ______ ____ _____ _______ ______ ______ _____ ______ _________ ___.
____ ____ _______ __________ _________ _____ _________ _________ ____ ________ _____.
__________ _______ ________ _______ ______ _________ _____.
___ ____ ________ _________ ______ __________ ______.
_________ _________ ___ __________ _________ __________ ______ _________ __________.
_______ ______ __________ ___ _____ ______.
_______ ____ _______ ____ ___ ______ ___ __________ ___.
____ _________ _____ ________ ______.
_______ __________.
Get Full Answer on WhatsApp