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Jawaban Soal Matematika Terapan: X Dy DX y X

The document contains the solutions to two applied mathematics problems: 1) Solving a first order linear differential equation to find the general solution y in terms of x. 2) Solving another first order linear differential equation to find an expression for y in terms of x and natural logarithm functions.

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57 views3 pages

Jawaban Soal Matematika Terapan: X Dy DX y X

The document contains the solutions to two applied mathematics problems: 1) Solving a first order linear differential equation to find the general solution y in terms of x. 2) Solving another first order linear differential equation to find an expression for y in terms of x and natural logarithm functions.

Uploaded by

trisnadewi
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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KELAS 2.

KIA
1. TRISNA DEWI
2. UTARI OKTAVIA
3. VIRWINDICA BELLA HINGGIS

JAWABAN SOAL MATEMATIKA TERAPAN

14)

dy
2
3
+(23 x ) y=x
dx
dy
2
3
+( 23 x ) y=x
dx
x3

dy (23 x ) y
+
=1
dx
x3

(23 x )
x3

P(x) =
Q(x) = 1

p dx

FI = e

y.FI =

= e

(23 x )
dx
3
x

1 2
x 3 ln x
= 2
e

Q ( x ) FI dx

1 2
x 3 ln x dx
2
y.FI =
1. e

y.FI =

x3
2
23 x

1 2
x 3 ln x
. 2
e

+C

y=

15)

1 2
x 3 ln x
2
x3
+C . e
2
23 x

dy y
+
=1
dx ln x
dy y
+
=1
dx ln x
x

P(x) =

1
x ln x

Q(x) =

1
x

FI = e

p dx

x ln1 x dx

Q ( x ) FI dx

y.FI =

x . eln ln x dx

y.FI = ln xe

ln ln x

ln ln x
1
e
+C
x ln x

ln xe ln ln x
1 e ln ln x
C

. ln ln x + ln ln x
ln ln x
x ln x e
e
e

y = ln |x| -

16)

ln ln x
= e

= e

y.FI =

y=

dy
y
1
+
=
dx x ln x x

1
ln ln x
+C e
x ln x

x dy 2 y dx=(x2) e x dx

( x 2)e
2y
dy
dx=
dx
x
x

dx

x dy2 y dx=( x2) e dx


x

dy 2 y ( x 2)e
=
dx x
x

P(x) =

2
x

( x2)e x
Q(x) =
x

FI = e

y.FI =

p dx

dx
2
x

= e

2 ln x

Q ( x ) FI dx
x

( x2)e 2
. x dx
y.FI =
x

y.FI =

x e x x 2 2e x x2

+C
( x2) (x3)
x

y=

xe
2e

+C x 2
( x2) (x3)

y=

x 2 e x 5 x e x + 4 e x
2
+C x
2
x 5 x +6

( x2) e
dx
x3

x2

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