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Quiz 3: Week 2 of ODEs, Cheat Sheet of Mechanical Engineering

For Ordinary Differential Equations continuing education UCSD

Typology: Cheat Sheet

2024/2025

Uploaded on 02/09/2025

katy-wicks
katy-wicks 🇺🇸

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Week 2, Chapter 1: First-Order ODEs
Quiz 3
Name
Points earned /15
AI usage is strictly forbidden. Show all transitioning steps and box in all solutions. After the
completion of the quiz, please submit the scan in PDF form.
1) Solve 3x2y0=2xy +6y2.
1
/
(3x
y
=
2xy
+
6y2)
u
=
x
F2(x
*
dx
+
c)
=
u
=
x
f
-
2
-
+
c)
Y
=
xy
+
2
-
g
y Py
=
yz
we
e
u
=
x
(6x
+
c)
-
u
=
y
-
+
=
y
=
y
=
1
u
=
c
+
6
x
Y
x
U
+
(
-
ap4
=
(
-
2)g
1
c
+
6
x
-
-
i
+
(1
-
2)
+x)u
=
(1
-
2)
y
=
x
+
=_
Liner
x
*
DE
-
h
=
[pdx
=
Ex
=
Lux
=
Lnx
y
=
c
+
x
u
=
(ferdx
+
c)
=
=
(x5
+
6
x
=j
Luxelfdx
+
Tx
y
=
G
+
5
*
=
x
f
2/x*
.
x
dx
+
c)
=
*
=
E
+
C
3
*
pf2

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Week 2, Chapter 1: First-Order ODEs

Quiz 3

Name Points earned / AI usage is strictly forbidden. Show all transitioning steps and box in all solutions. After the completion of the quiz, please submit the scan in PDF form. 1) Solve 3 x^2 y^0 = 2xy + 6y^2. 1 /

(3x y

=

2xy

6y2)

u =^ x F2(x

dx +^ c) =

u = x f

2 -^ +^ c)

Y

=

xy +^2 -

g

y Py

=

yz

wee

u =^ x(6x +^ c)

u =

y

  • (^) +

y

=

y

= (^1) u = c +^6 x

Y x

U+( -

ap

= (

2)g

1 c + (^6) x

-^ -

i+(1 - 2) +x)u =

y

=

x

+ =_Liner x

*DE

h =

[pdx

=

Ex=

Lux =^ Lnx

y

= c

x

u = (ferdx +^ c) =^

= (x5 +^6 x

=jLuxelfdx+ Tx

y

=

G+^5

x f2/x*.^ x^ dx+^

c)

=

=

E+ C^3 *

Week 2, Chapter 1: First-Order ODEs 1) Solve 3 x^2 y^0 = 2xy + 6y^2. 2