Solve differential equation xy'= 6y+12x^4 y^(2/3)

Yasmin 2020-11-09 Answered
Solve differential equationxy=6y+12x4y(2/3)
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Expert Answer

estenutC
Answered 2020-11-10 Author has 81 answers

dy/dx+P(x)y=Q(x)yn
n=0 or n=1
Substituting v=y1n transforms the above equation into the linear equation
(dv)/dx+(1n)P(x)v=(1n)Q(x)
(dv)/dx+P(x)y=Q(x)
y(x)=e(P(x)dx)[(Q(x)e(P(x)dx))dx+C]
The differential equation is,
xy=6y+12x4y(2/3)
The above equation can be written as follows
y6/xy=12x3y(2/3)
Substituting v=y12/3 or y 1/3 transforms the above Bernoulli equation into the linear equation
(dv)/dx2/xv=4x3
v(x)=e((2/x)dx)[(4x3e((2/x)dx))dx+C]
=e(2lnx)[(4x3x2lnx)dx+C]
=x2[4x2/x+C]
v(x)=2x4+Cx2
y1/3=2x4+Cx2
y(x)=(2x4+Cx2)3
where C is constant

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Jeffrey Jordon
Answered 2021-10-22 Author has 2087 answers

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