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From (1) (Y + x*y +2x2) dx +(x + 4×y" + ® y³) dy = 0 - ydx + xydx + 2x²dx + xdy + 4xy"dy +oyy =(Y.dx + xdy) +(x³y dx + 4xy* dy)+ 2 x²dx + ®ydy We have dlxy) = Xdy + ydx = Ydx + xdy , than d(xy) + xy(x²dx + 4y3dy) + 2 x°dx + 8 y³dy=o 43) Wle have d(x3) dx = 3x2 > dCx3) 3x?d x -d(x3) = x²dx Smilarly (y") = 4y =) d(y") = 4y%dy d(y) = yay (5)

From (1) (Y + x*y +2x2) dx +(x + 4×y" + ® y³) dy = 0 - ydx + xydx + 2x²dx + xdy + 4xy"dy +oyy =(Y.dx + xdy) +(x³y dx + 4xy* dy)+ 2 x²dx + ®ydy We have dlxy) = Xdy + ydx = Ydx + xdy , than d(xy) + xy(x²dx + 4y3dy) + 2 x°dx + 8 y³dy=o 43) Wle have d(x3) dx = 3x2 > dCx3) 3x?d x -d(x3) = x²dx Smilarly (y") = 4y =) d(y") = 4y%dy d(y) = yay (5)

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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Can anyone explain to me in words, the steps that happened in this process? I find it hard to understand. Thank youuu.

From (1) (Y + x*y +2x2) dx +(x + 4×y" + ® y³) dy = 0 - ydx + xydx + 2x²dx + xdy + 4xy"dy +oyy =(Y.dx + xdy) +(x³y dx + 4xy* dy)+ 2 x²dx + ®ydy We have dlxy) = Xdy + ydx = Ydx + xdy , than d(xy) + xy(x²dx + 4y3dy) + 2 x°dx + ® y³dy=o 43) Wle have d(x3) dx = 3x2 > dCx3) 3x?d x -d(x3) = x²dx Smilarly (y") = 4y =) d(y") = 4y%dy d(y) = yay (5)
Transcribed Image Text:From (1) (Y + x*y +2x2) dx +(x + 4×y" + ® y³) dy = 0 - ydx + xydx + 2x²dx + xdy + 4xy"dy +oyy =(Y.dx + xdy) +(x³y dx + 4xy* dy)+ 2 x²dx + ®ydy We have dlxy) = Xdy + ydx = Ydx + xdy , than d(xy) + xy(x²dx + 4y3dy) + 2 x°dx + ® y³dy=o 43) Wle have d(x3) dx = 3x2 > dCx3) 3x?d x -d(x3) = x²dx Smilarly (y") = 4y =) d(y") = 4y%dy d(y) = yay (5)
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