Question

can i transpose variables in differential equations?
x^2 dx + y (x – 1) dy = 0
i want to do this using separation metthod
i want to know if it is possible to transpose
y(x-1)dy to te other side
hence looking lke this after
x2 dx + = -y(x+1)dy

Answer 1

yes thats legit in solving separable eqns

Answer 2

\[\large x^2 \mathrm{d} x + y (x – 1) \rm{d}y = 0\]

\[\large x^2 \mathrm{d} x = y (x – 1) \rm{d}y \]

\[\large \dfrac{x^2}{x-1}~ \mathrm{d} x = y ~ \rm{d}y \]

Answer 3

\[\large \int \dfrac{x^2}{x-1}~ \mathrm{d} x = \int y ~ \rm{d}y \]

Answer 4

you da real mvp thanks, really helped and appreciate it thanks sir :))

Answer 5

np :) notice you may need to reduce the degree of numerator using long division for integrating left side integral

Answer 6

yep, noted thanks sir