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CrazyAzn89
Lv 5
I need help with differential equations?
How to solve this differential equation using separation of variables?
2dy/dx = y(x+1) / x
3 Answers
Relevance
- mohanrao dLv 710 years agoFavourite answer
2 dy/dx = y(x+1) / x
separating variables
2 dy/y = (x + 1) dx / x
=> 2 dy/y = (1 + (1/x) ) dx
integrating both sides
2 ln y = x + ln x + c
=> ln y^2 - ln x = x + c
=> ln[ y^2 / x) = x + c
=> y^2/x = e^(x+c)
=> y^2 / x = Ce^x
=> y^2 = C x e^x
y = ±√(Cxe^x)
- MechEng2030Lv 710 years ago
2(dy/dx) = y(x + 1)/x
2/y dy = (x + 1)/x dx
Integrating both sides:
2*ln|y| = x + ln|x| + C
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