Answer to Question #223114 in Differential Geometry | Topology for Vectors

Question #223114

Find the general solution of these differential equations.

3) dy/dx = cosx/y 4) dy/dx = 4x/ey 5) x+4ydy/dx = 0



1
Expert's answer
2021-09-13T00:03:04-0400

3)


"dy\/dx=\\cos x\/y"

"ydy=\\cos xdx"

Integrate


"\\int ydy=\\int\\cos x dx"

"\\dfrac{y^2}{2}=\\sin x+\\dfrac{1}{2}C"

The general solution is

"y^2=2\\sin x+C"

Or


"y^2-2\\sin x=C"

4)


"dy\/dx=4x\/e^y"

"e^ydy=4 xdx"

Integrate


"\\int e^ydy=\\int4 x dx"

"e^y=2x^2+C"

The general solution is

"e^y=2x^2+C"


Or


"e^y-2x^2=C"

5)


"x+4ydy\/dx=0"

"4ydy=- xdx"

Integrate


"\\int 4ydy=-\\int x dx"

"2y^2 =-\\dfrac{x^2}{2}+\\dfrac{1}{2}C"

The general solution is

"4y^2=-x^2+C"

Or


"4y^2+x^2=C"


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