Solve. dy/dx+3/x y = 27y^(1/3) 1n(x), x > 0

Tobias Ali 2021-02-05 Answered
Solve. dydx+3xy=27y131n(x),x>0
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Expert Answer

Talisha
Answered 2021-02-06 Author has 93 answers
Here the given differential equation is
y+3yx=27y13
Let v=y23thendvdx=23y13dydx.With respect to this transformation, the above DE reduces to 32y13dvdx+3yx=27y13
32dvdx+3y23x=27
12dvdx+y23x=9
dvdx+2y23x=18
dvdx+2vx=18
x2dvdx+2xv=18x2
ddx(x2v)=18x2
x2v=18x2dx+c
x2v=6x3+c
v=6x+cx2
y23=6x+cx2
y=(6x+cx2)32
Where c is arbitrary constant.
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