Solve differential equation xy'+3y=6x^3

cistG 2020-12-30 Answered
Solve differential equationxy+3y=6x3
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Expert Answer

Usamah Prosser
Answered 2020-12-31 Author has 86 answers

xdydx+3y=6x3
Divide by 'x'
xdydxx+3yx=6x3x
dydx+3xy=6x2 (1)
Compare (1) with dydx+P(x)y=Q(x) we have
P(x)=3x, Q(x)=6x2
I.F.=eP(x)dx
=e31xdx
=e3ln(x) (1x=ln(x))
I.F.=elnx3 (nlnx=lnxn)
I.F.=x3
y(I.F.)=Q(x)(I.F.)dx
yx3=6x2x3dx
x3y=6x5dx (aman=am+n)
andx=an+1n+1
x3y=6(x5+15+1)+C
x3y=6(x66)+C
x3y=x6+C
y=x6x3+Cx3
y=x3+Cx3

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Jeffrey Jordon
Answered 2021-12-25 Author has 2262 answers

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