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У(у? + 1)dx + x(у? — 1)dy %3D 0 ySinydx + x(Siny - у Сosy)dy %3D 0

У(у? + 1)dx + x(у? — 1)dy %3D 0 ySinydx + x(Siny - у Сosy)dy %3D 0

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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Solve the following DE's using Integrating Factor by Inspection or by applying Table 1. y(y? + 1)dx + x(y² – 1)dy = 0 ySinydx + x(Siny – y Cosy)dy = 0
Transcribed Image Text:Solve the following DE's using Integrating Factor by Inspection or by applying Table 1. y(y? + 1)dx + x(y² – 1)dy = 0 ySinydx + x(Siny – y Cosy)dy = 0
ang oy dx – x dy x dy – ydx = d y dx –x dy ydx – x dy = d y? у dx - x dy xdy – ydx = d In xy xy Table 1 хdy - ydx x² + y? 1 y dx – x dy = d arctan x² + y* ydx+ xdy y dx + x dy d(In xy) %3D ху xy y dx + xdy -1 y dx +x dy n>1 (ху)"" = d (ху)" (n– 1)(xy)"- ydy + xdx x² + y° 1 у dy +x dx x² + y? =d In(x + y) ydy + x dx = d 1 -1 у dy +x dx n>1 (x² + y°)"° (x² + y*)" 2(n – 1)(x² + y³)*-! ay dx + bx dy (a, b constants) xly(ay dx + bx dy) = d(xªy")
Transcribed Image Text:ang oy dx – x dy x dy – ydx = d y dx –x dy ydx – x dy = d y? у dx - x dy xdy – ydx = d In xy xy Table 1 хdy - ydx x² + y? 1 y dx – x dy = d arctan x² + y* ydx+ xdy y dx + x dy d(In xy) %3D ху xy y dx + xdy -1 y dx +x dy n>1 (ху)"" = d (ху)" (n– 1)(xy)"- ydy + xdx x² + y° 1 у dy +x dx x² + y? =d In(x + y) ydy + x dx = d 1 -1 у dy +x dx n>1 (x² + y°)"° (x² + y*)" 2(n – 1)(x² + y³)*-! ay dx + bx dy (a, b constants) xly(ay dx + bx dy) = d(xªy")
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