dentity the type and determine the linearity of the given differential equation, and also give its order and degree. 1. x²y" + xy' = x² + y dCA dt 2. 3. dx² a² y at² -RCA0et-k₂C² 5 d3 dx3 -3x y a²0² y dx² =xlnx 5. xsin y'=y"e*+y 6. 5+(y)2 =[3z³y² + (y")³14/3 aw at 4 =h402 w əs² 8. xyzx +2y³ (2)³ = 1 7.

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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I. For each give DE, determine the dependent variables and independent variables.
Identify the type and determine the linearity of the given differential equation, and
also give its order and degree.
1. x²y" + xy = x² + y
dCA-RC A0e
kC
dt
2.
3.
4.
d²y
dx²
0² y
at²
5
-a
-kyt-k₂C²³₁
d³ y
dx.3
-3x¹y
= xln x
a ²0²,
2
?х²
II. Verify if the given function is a solution of the indicated differential equation.
5. xsin y'=y"e*+y
6. 5+(y)² =[32³ y² + (y")³]4/3
√√
2cosh
a4w
=h4
at = h1d²
ds2
8. xyz +2y³(z„)³ =1
7.
1. xy³ + y²-x)dx-ydy=0
-2=cxy; (x²
2. y = Insin(x - A) + B; y" + (y)² +1=0
3. y = ae³* +be 3x; y"-9y=0
4. y=q₁x+c₂e; (x+1)y" + xy'-y=0
Transcribed Image Text:I. For each give DE, determine the dependent variables and independent variables. Identify the type and determine the linearity of the given differential equation, and also give its order and degree. 1. x²y" + xy = x² + y dCA-RC A0e kC dt 2. 3. 4. d²y dx² 0² y at² 5 -a -kyt-k₂C²³₁ d³ y dx.3 -3x¹y = xln x a ²0², 2 ?х² II. Verify if the given function is a solution of the indicated differential equation. 5. xsin y'=y"e*+y 6. 5+(y)² =[32³ y² + (y")³]4/3 √√ 2cosh a4w =h4 at = h1d² ds2 8. xyz +2y³(z„)³ =1 7. 1. xy³ + y²-x)dx-ydy=0 -2=cxy; (x² 2. y = Insin(x - A) + B; y" + (y)² +1=0 3. y = ae³* +be 3x; y"-9y=0 4. y=q₁x+c₂e; (x+1)y" + xy'-y=0
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