Dy In (y) == 9/²+c e e t y = e yz ce 9₁= - 96- eft U 63 7 Se d t Le 21 63t e 21 636 + C 21 + C + c 17 M/2 11i (-3,63 +76) 17

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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First Order Equations-Nonlinear Bernoulli: Problem 3

 

 

Problem 3
Find the general solution for the following
differential equation
y² + 9y = -3y6 y't ag=
ay
*
y²tqy 20
y = gy+gy
y' =_ 9 y
у
y'
= -4
- dy
५ तह
Fydy = 5.90€
dt = -967
In (y) == 9+c
e
e
at Co
e e
- 9€-
у
y =
y z ce
4₁ = 69€
e
U² =
آن
1
Je
مال
۲-۱۲-۱
(f(x)y,
6
ما الله
F(t)=-3
-6-2
do
to d6 = 5-3/e tej de
Ne
21
06ے ہیں
PCE) e
Le
#Scºde
eo
21
63t
21
63€
e
21
7
4€
y
1 ² = √5-36@²²4) ²³ de 9 = (36²t +7c" (6-7)
7
-at
+ C
-3-636,
General Solution
J
Y = Uy₁
4
+€
-at
y₁ = e
U= 63× du= 63
I do
63
7
U
7
H
+ c)
(07²/4 7c) ²/² v = (-36²° +7c)"
Transcribed Image Text:Problem 3 Find the general solution for the following differential equation y² + 9y = -3y6 y't ag= ay * y²tqy 20 y = gy+gy y' =_ 9 y у y' = -4 - dy ५ तह Fydy = 5.90€ dt = -967 In (y) == 9+c e e at Co e e - 9€- у y = y z ce 4₁ = 69€ e U² = آن 1 Je مال ۲-۱۲-۱ (f(x)y, 6 ما الله F(t)=-3 -6-2 do to d6 = 5-3/e tej de Ne 21 06ے ہیں PCE) e Le #Scºde eo 21 63t 21 63€ e 21 7 4€ y 1 ² = √5-36@²²4) ²³ de 9 = (36²t +7c" (6-7) 7 -at + C -3-636, General Solution J Y = Uy₁ 4 +€ -at y₁ = e U= 63× du= 63 I do 63 7 U 7 H + c) (07²/4 7c) ²/² v = (-36²° +7c)"
Find the general solution for the following differential equation:
y' +9y = -3/1/
General Solution: y(t) = (-3e6³t+7c)²(e-⁹¹)
(9
Transcribed Image Text:Find the general solution for the following differential equation: y' +9y = -3/1/ General Solution: y(t) = (-3e6³t+7c)²(e-⁹¹) (9
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