Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
STRICTLY HANDWRITTEN THEN BOX THE FINAL ANSWERS
Transcribed Image Text:Find the general solution for the following differential equations
1. 2y" + 18y = 6tan 3x
2. (D-1)² = +1
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Follow-up Question
CAN YOU RE-ANSWER #1 USING THE AUXILIARY METHOD OR SOMETHING? PLS SEE THE EXAMPLES IN THE PHOTOS.
Transcribed Image Text:Name:
& Year
No.:
ger
2
11
y
U
m
√=
2X
-"ye = C₁ e²
2 -4m + 4
+ 4x + 4 =
(m - 2)² = 0
m = 2,2
4y + 4 =
w = | 2 0 ²x
22x
W
W, =
W =
11/2
2X
fp = A ₂ ²x + B xe ²x
4x
QY
e
x ²+1
-xe
2x
2xe ²x te"
- (2 x=²*+e ²*) (e²*)-(xe²*) (²²)
2x+24x-2x64*
x² +1
2x
e
20²
th2 xe
y²+1
tet
2Y
e zy
x²+)
2x e²x te ²x
-((e²*) (1)
2/x
2X
2X
x²+1
= (E¹) (47₁) - O
e
A
B'
ур
W₁
CI
W
I
·S.
W2
W
-xeyr
X
#S
(1
u
F
let y = x² +1
- 1/2/3 in 1x² +11
الاول
In/ x
=
du = 2x dx = -du-xd x
-—-—- Irku)
B () = 7+1
arctan ()
=
2
xet
+ 1
X
x ²+1
e
2x
t(arctanle) xẻ
xe
2x
2 X
yp=== Infr²+1/e²x + artan (x) xe²
у = ус тур
2X
2X
2x
Ty = G₁ e ²x + 6₁₂ xe ²x - 2/2 In / x ² + 1/ e²
tartant) xe
![_L (D) y)=P(x)
_Yc = C₁ y₁ + C₂Y₂
Variation of Parameters
Yp = V₁ U₁ + V₂ Y₂
_y' = U₁ y'₁ + U₁' Y₁ + Ua Ya ₁ + Uz ¹ Y ₂
tet:
+
_y₁ = U₁ y ₁"' + n₂ Yo'
y " = U₁ y ₁ " + U ₁ Y ₁ + Uz Y₂" + la! Yo!
L (D)y p(x)
ay" +by' + cy = P(X)
_y² + y = tan Ⓡx
AE: m² + 1 = 0
ma=-1
U₂¹=vPC x -cos X
| U₂ = in /vec x ttany [-viny
-Wivinx + U₂' cos x = tan ex
U₁' cor x + y₂' vin x = D.
U₁' cor x = - U₂' viny
U₁' = -U₂¹ VINY
сок у
-U₁ 'vin x cos x + 4₂' car @ x = tan ex corx
U₁' cor x vin x + U₂'sin 2 y = 0
1
ष
Ug
car 2x + vin ³ x ] = [ vin x 78 car
corx
|u₂¹ =
cor²x
corx
=
_U₁' =
U₁
_y₁ = -1₁ vin x +U₂ cov X
_y"=-u₁' vinx - U₁ corx + - U₂ rin x + U ₂¹ cos x)
U₁'= -vin³x -(1-corex ) viny
corax
covo X
I
vin x
[uery]
vindy [UIAY
cory
m = ± 1
Fur: fear x₁ vinx }
|Y₁ = C₁ car x 1 C₂ vinx
y = U₁ corx tuasiny
Up = U₁ cor x + l₂ vin x
y = (-vec x - car x) carx + (in /vecx + tanx)
vin x) rin x
1x|-
_y₁ = U₂₁ [-vin x) + U₁ CDs x tua (carx) + ug 'vinx y = recxcorx-cor@x+rin x In | rec x + ten x / -sin ³x
U₁' cos x + la vin x = 0
y = -(cor+) (cos x) - cas @x-sm x + vinx (n / vecxtanx/
y = -1 -1 +0A x In reaat tany
| Yp = sinx in /vec x tany -
-2
vin x-viny cov? X
cov oy
sinx
CONX
tan x vecx trinx
=-vecy - corx
"1
_y" + y = tan@ x
(-U₁' vin x - U1₁ cor x - U₂ vin x + U₂¹ carx) + (U₁corx + U₂ sin x) = tan@ y
7 car x
(Coxx) xinx ]
y = c₁ cv x + Coviny + vin x / n /recx+tan/₂
Y
blueberry](https://content.bartleby.com/qna-images/question/766c4be6-8af2-4ce7-931f-8cc1ca150002/49f35204-e783-4b8e-ad06-9c46c0ea4ca2/aihw455_processed.jpeg)
Transcribed Image Text:_L (D) y)=P(x)
_Yc = C₁ y₁ + C₂Y₂
Variation of Parameters
Yp = V₁ U₁ + V₂ Y₂
_y' = U₁ y'₁ + U₁' Y₁ + Ua Ya ₁ + Uz ¹ Y ₂
tet:
+
_y₁ = U₁ y ₁"' + n₂ Yo'
y " = U₁ y ₁ " + U ₁ Y ₁ + Uz Y₂" + la! Yo!
L (D)y p(x)
ay" +by' + cy = P(X)
_y² + y = tan Ⓡx
AE: m² + 1 = 0
ma=-1
U₂¹=vPC x -cos X
| U₂ = in /vec x ttany [-viny
-Wivinx + U₂' cos x = tan ex
U₁' cor x + y₂' vin x = D.
U₁' cor x = - U₂' viny
U₁' = -U₂¹ VINY
сок у
-U₁ 'vin x cos x + 4₂' car @ x = tan ex corx
U₁' cor x vin x + U₂'sin 2 y = 0
1
ष
Ug
car 2x + vin ³ x ] = [ vin x 78 car
corx
|u₂¹ =
cor²x
corx
=
_U₁' =
U₁
_y₁ = -1₁ vin x +U₂ cov X
_y"=-u₁' vinx - U₁ corx + - U₂ rin x + U ₂¹ cos x)
U₁'= -vin³x -(1-corex ) viny
corax
covo X
I
vin x
[uery]
vindy [UIAY
cory
m = ± 1
Fur: fear x₁ vinx }
|Y₁ = C₁ car x 1 C₂ vinx
y = U₁ corx tuasiny
Up = U₁ cor x + l₂ vin x
y = (-vec x - car x) carx + (in /vecx + tanx)
vin x) rin x
1x|-
_y₁ = U₂₁ [-vin x) + U₁ CDs x tua (carx) + ug 'vinx y = recxcorx-cor@x+rin x In | rec x + ten x / -sin ³x
U₁' cos x + la vin x = 0
y = -(cor+) (cos x) - cas @x-sm x + vinx (n / vecxtanx/
y = -1 -1 +0A x In reaat tany
| Yp = sinx in /vec x tany -
-2
vin x-viny cov? X
cov oy
sinx
CONX
tan x vecx trinx
=-vecy - corx
"1
_y" + y = tan@ x
(-U₁' vin x - U1₁ cor x - U₂ vin x + U₂¹ carx) + (U₁corx + U₂ sin x) = tan@ y
7 car x
(Coxx) xinx ]
y = c₁ cv x + Coviny + vin x / n /recx+tan/₂
Y
blueberry
Solution
by Bartleby ExpertFollow-up Question
pls answer #2. STRICTLY HANDWRITTEN THEN BOX THE FINAL ANSWERS
Solution
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