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50. y" = (x + y')²

50. y" = (x + y')²

Advanced Engineering Mathematics
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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Find a general solution of each reducible second-order differ- ential equation in Problems 43-54. Assume x, y and/or y' positive where helpful (as in Example 11). 43. ху" — у 45. y" + 4y = 0 47. y" = (y')? 49. yy" + (y')² = yy' 51. y" = 2y(y') 44. yy" + (y')2 = 0 46. xy"+y 4x 48. x²y" + 3xy' = 2 50. y" = (x+ y')? 52. y'y" = 1 54. уу" 3 3(у')? %3D %3D %3D %3D %3D 55. Show that the substitution v = ax + by + c transforms the differential equation dy/dx = F(ax + by + c) into a separable equation. %3D
Transcribed Image Text:Find a general solution of each reducible second-order differ- ential equation in Problems 43-54. Assume x, y and/or y' positive where helpful (as in Example 11). 43. ху" — у 45. y" + 4y = 0 47. y" = (y')? 49. yy" + (y')² = yy' 51. y" = 2y(y') 44. yy" + (y')2 = 0 46. xy"+y 4x 48. x²y" + 3xy' = 2 50. y" = (x+ y')? 52. y'y" = 1 54. уу" 3 3(у')? %3D %3D %3D %3D %3D 55. Show that the substitution v = ax + by + c transforms the differential equation dy/dx = F(ax + by + c) into a separable equation. %3D
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