Show that the first order differential equation (x + 1)y'-3y= (x+1)^5 is of the linear type. Hence solve for y given that y = 1.5 when x = 0

Dillard 2021-01-15 Answered
Show that the first order differential equation (x+1)y3y=(x+1)5 is of the linear type.
Hence solve for y given that y = 1.5 when x = 0
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Expert Answer

Asma Vang
Answered 2021-01-16 Author has 93 answers

(x+1)y3y=(x+1)5
y3(x+1)y=(x+1)4
Compare with
y+P(x)y=Q(x)
P(x)=3x+1
Q(x)=(x+1)4
Hence given differential equation is of the linear type
I.F.=eP(x)dx
=e3x+1dx
=e3ln(x+1)
=eln(x+1)3
=(x+1)3
yI.F.=Q(x)I.F.dx
y(x+1)3=(x+1)4(x+1)3dx
y(x+1)3=(x+1)dx
y(x+1)3=x22+x+C
y=(x22+x+C)(x+1)3
y(0)=1.5
(0+0+C)(0+1)3=1.5
C=1.5
y=(x22+x+1.5)(x+1)3

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