Find general solutions (implicit if necessary, explicit if convenient) of

eliaskidszs 2021-12-28 Answered
Find general solutions (implicit if necessary, explicit if convenient) of the differential equations in Problem. Primes denote derivatives with respect to x.
dydx=(64xy)13
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deginasiba
Answered 2021-12-29 Author has 31 answers
dyy13=(64)13(x13)dx
dyy13=4(x13)dx
3y232=34x434+C
3y232=3x43+C
y23=2x43+23C
y=(2x43+23C)32
Here, C is the constant of integration,
Suppose 23 is equal to another constant D
Rewrite the solution as
y=(2x43+D)32 which is the general explicit solution the given differential equation.
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temnimam2
Answered 2021-12-30 Author has 36 answers
x(79)=139
67100=0
4(ln(x))3
p=wf
6.512=0
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karton
Answered 2022-01-09 Author has 439 answers

dydx=(64xy)13=4x13y13
or, y13dy=4x13dx
Integrating, we get,
y13dy=4x13dx
or, y13+113+1=4x13+113+1+c
or, y2323=4x4343+c
or, 32y2/3=3x4/3+c
which is the required general solution, where c be an arbitrary constant.
(1+x)dydx=4y
or, dyy=4dxx+1
Integrating, dyy=4dxx+1
or, ln|y|=4ln|x+1|+lnc
or, y=c(x+1)4
Required general solution:
y=c(x+1)4 where c be an arbitrary constant.

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