Find the general solution of these differential equations.
3) dy/dx = cosx/y 4) dy/dx = 4x/ey 5) x+4ydy/dx = 0
3)
"ydy=\\cos xdx"
Integrate
"\\dfrac{y^2}{2}=\\sin x+\\dfrac{1}{2}C"
The general solution is
"y^2=2\\sin x+C"Or
4)
"e^ydy=4 xdx"
Integrate
"e^y=2x^2+C"
The general solution is
"e^y=2x^2+C"Or
5)
"4ydy=- xdx"
Integrate
"2y^2 =-\\dfrac{x^2}{2}+\\dfrac{1}{2}C"
The general solution is
"4y^2=-x^2+C"Or
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