25. y (xy + y)(1 +x)/2=
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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please send handwritten solution for Q 25 1.6
Transcribed Image Text:1.6 Problems
Find general solutions of the differential equations in Prob-
lems i through 30. Primes denote derivatives with respect to x
throughout.
15. x(x + y)y' + y(3x + y) = 0
16. y = Vx + y +1
18. (x + y)y = 1
20. y?y' + 2xy = 6x
22. x'y + 2xy = 5y*
24. 2xy' + y'e-24 = 2xy
25. y?(xy' + y)(1 +x*)/2 = x
26. 3y?y' + y' = e*
27. 3xyy = 3x* + y
28. xe' y = 2(e +x'e)
29. (2x sin y cos y)y' 4x +sin' y
30. (x +e)y' = xe – 1
17. y = (4x + y)?
19. xy' + 2ry 5y
21. y' = y + y
23. xy' + 6y = 3xyt/3
1. (x + y)y = x - y
3. xy = y +2xy
5. x(x+ y)y' = y(x – y) 6. (x + 2y)y' y
7. xy'y' = x + y
9. x'y = xy + y
11. (x² – y?)y = 2ry
12. xyy' = y? + x/4x? + y?
13. xy = y +Vr + y?
14. yy +x = x² + y?
2. 2xyy' = x? + 2y?
4. (x - y)y' = x+ y
%3D
8. x'y' = xy + x'erla
10. xyy' = x? +3y?
1.6 Substitution Methods and Exact Equations 73
In Problems 31 through 42, verify that the given differential
equation is exact; then solve it.
60. Use the method in Problem 59 to solve the differential
equation
dy
2y-x +7
31. (2x + 3y) dx + (3x +2y) dy = 0
32. (4x - y) dx + (6y – x) dy = 0
33. (3x? +2y?) dx+ (4xy +6y?) dy = 0
34. (2xy + 3x?) dx + (2x'y+4y) dy = 0
35. (x' +2) dx + (y² + In x) dy = 0
dx 4x – 3y – 18
61. Make an appropriate substitution to find a solution of the
equation dy/dx = sin(x – y). Does this general solution
contain the linear solution y(x) = x - 1/2 that is readily
verified by substitution in the differential equation?
62. Show that the solution curves of the differential equation
36. (1 + ye") dx + (2y + xe) dy = 0
y(2r - y)
x(2y3 - x)
37. (cos x + In y) dx +
dy = 0
dy
dx
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