What is a general solution to the differential equation y'=5x^(2/3)y^4?

sincsenekdq

sincsenekdq

Answered question

2022-09-04

What is a general solution to the differential equation y = 5 x 2 3 y 4 ?

Answer & Explanation

Ashlynn Cox

Ashlynn Cox

Beginner2022-09-05Added 12 answers

d y d x = 5 x 2 3 y 4

This is a First Order separable DE, so collecting like terms and "separating the variables" we get;

y - 4 d y = 5 x 2 3 d x

Integrating we get:

y - 3 - 3 = 5 x 5 3 5 3 + C 1
y - 3 = - 9 x 5 3 - 3 C 1
1 y 3 = - 9 x 5 3 + C
y 3 = 1 C - 9 x 5 3
y = 1 C - 9 x 5 3 3

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