EXERCISES 3.2 In Exercises 1-4, determine if the differential equation is separable. 1. y' = x cos y + 2xy2 2. 3xy? dx - 6 sin y dy =0 dy 3. dx x²+2xy 4. sin xy' xy + 4x %3D %3D Solve the differential equations in Exercises 5-12. 5. y' = 2r?y – 4y 7. (x² + 1) 6. e*y dx+4y dy = 0 %3D dy d = xy² +x 8. sec xy' – xy/(y + 4) = 0 9. e* (y² – 4y) dx+4 dy = 0 dy x²y³ +3xy³3 2x?y 10. dx 11. t dt dy, dy = te dt dr =r sin 0 de 12. (r + 1) cos 0 Solve the initial value problems in Exercises 13-16. 13. y' + x²/y = 0, y(0) = 1 dy 14. 3 = 2xy – y, y(2) = 1 dx %3D dy 15. dx 4ху y2 +4' ,y(1) = 1
EXERCISES 3.2 In Exercises 1-4, determine if the differential equation is separable. 1. y' = x cos y + 2xy2 2. 3xy? dx - 6 sin y dy =0 dy 3. dx x²+2xy 4. sin xy' xy + 4x %3D %3D Solve the differential equations in Exercises 5-12. 5. y' = 2r?y – 4y 7. (x² + 1) 6. e*y dx+4y dy = 0 %3D dy d = xy² +x 8. sec xy' – xy/(y + 4) = 0 9. e* (y² – 4y) dx+4 dy = 0 dy x²y³ +3xy³3 2x?y 10. dx 11. t dt dy, dy = te dt dr =r sin 0 de 12. (r + 1) cos 0 Solve the initial value problems in Exercises 13-16. 13. y' + x²/y = 0, y(0) = 1 dy 14. 3 = 2xy – y, y(2) = 1 dx %3D dy 15. dx 4ху y2 +4' ,y(1) = 1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:First Order Ordinary Differential Equations
Chapter 3
124
EXERCISES 3.2
In Exercises 1-4, determine if the differential equation
is separable.
1. y' = x cos y + 2xy²
2. 3xy? dx - 6 sin y dy = 0
dy x2 + 2xy
16. ye dy
17. a) Solve
for y.
b) Use th
4. sin xy' xy + 4x
of x fo
3.
dx
proble
Solve the differential equations in Exercises 5-12.
6. e* y dx+4y³ dy = 0
18. a) Solve
5. y' = 2x?y - 4y
dy
for y.
7. (x? + 1)
= xy + x
b) Use t
of x f
dx
8. sec xy' – xy/(y +4) = 0
9. e* (y² – 4y) dx +4 dy = 0
dy x?y + 3xy
2x?y
probl.
dy, dy
11. t
19. Use Map
age) to g
10.
dx
= te'
dt
dt
dr
=r sin 0
do
20. Use Map
age) to g
12. (r2 + 1) cos 0
21. a) Show
Solve the initial value problems in Exercises 13-16.
13. y' +x?/y = 0, y(0) = 1
separ
b) Show
dy
14. 3
= 2xy- y, y(2) = 1
conve
%3D
dx
a sep
dy
15.
dx
4xy
y2 +4 (1) = 1
c) Solve
3.3 EXACT DIFFERENTIAL EQUATIONS
In the last section we learned how to solve separ
we will consider a type of equation whose solt
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