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CrazyAzn89
Lv 5
Help with differential equations?
I need help solving this differential equation using separation of variables:
ydx + xdy = 3xydx
3 Answers
Relevance
- RapidfireLv 710 years agoFavourite answer
Solve this differential equation by separating the variables then integrating:
y dx + x dy = 3xy dx
y + x(dy / dx) = 3xy
x(dy / dx) = 3xy - y
x(dy / dx) = y(3x - 1)
dy / y = (3x - 1) / x dx
dy / y = (3 - 1 / x) dx
∫ 1 / y dy = ∫ (3 - 1 / x) dx
ln|y| = 3x - ln|x| + C
ln|y| = 3x + C - ln|x|
y = ℮^(3x + C - ln|x|)
y = ℮ᶜ℮^(3x) / x
y = C℮^(3x) / x
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