- Itxa Itya Seat Work 2 Solution This Is How You Should Solve Your Guiz 1 I Ya Dx 1 X Dy 0 When X0 Yol G 1 (312.03 KiB) Viewed 19 times
methods in solving for solutions of
differential equations of order one (i.e. Separable, Homogeneous,
Linear, Exact)
Please use the format given on the first picture. Thank you
Itxa + itya . SEAT WORK #2 SOLUTION (This is how you should solve your guiz) 1) (i+ya) dx + (1+x) dy = 0; when x0, yol G could also be expressed as when yco) * check first for what type of egin separable: if divided by Homogenous : (I tyas ( +x+y: By visual inspection dx dy City") dx + [i+x*) dy
-0 degre: I a T .: SEPARABLE not of the same degrees .. non . homogenous * Linear : check for Lincarity Exact check for (i+ye) dx + (1+x?) dy = 0 exactness a non-linear both in sy Msity N=1+x? because of the terms is deriving in y is driving inx x² and ya existing O'F : 0+2y O + ax at the same time axay I axay Not egual : not exact :: SOLVE AS SEPARABLE EQ'N. separated egin For particular soution dx when X= 0, yol: + dy Arotan (0) + Arctan (1) - & Do not forget to put your dy Calcu in RADIANT mode . when dealing with invesse * from integral Calculus : trigo functions du a arctan u to 0+ 0 ә*у It x2 itya + John Sanatuan 1.:C: since c = TA Arctan x + Arotany C G General Solution Arctan x + Arctany a 17 h 4 1. Additional solutions to differential equations A. Integrating factors found by inspection 1. y(x² + y2 – 1)dx + x(x² + y2 + 1)dy = 0 when y(1) = 0 + 2. y(x?y2 – 1)dx + x(x²y2 + 1)dy = 0 = =