Would you like to inspect the original subtitles? These are the user uploaded subtitles that are being translated: 1 00:00:02,270 --> 00:00:07,100 Everyone just wanted you a couple examples of determining whether a differential equation is linear 2 00:00:07,100 --> 00:00:08,690 and why or it's not. 3 00:00:08,690 --> 00:00:09,830 And finding the order. 4 00:00:09,830 --> 00:00:13,280 So first of all the order is the order of the highest derivative. 5 00:00:13,460 --> 00:00:18,440 So in this case the biggest derivative is the second derivative it's the order of the highest derivative. 6 00:00:18,440 --> 00:00:19,750 So the order is to. 7 00:00:20,090 --> 00:00:23,720 In this case the order of the highest derivative would be three. 8 00:00:23,830 --> 00:00:26,440 And in this case the city why X to the fifth power. 9 00:00:26,810 --> 00:00:29,230 So the order of the highest rated is 1. 10 00:00:29,830 --> 00:00:30,590 OK. 11 00:00:30,950 --> 00:00:33,300 As far as linear and non-linear in Y. 12 00:00:33,320 --> 00:00:35,630 So a differential equation is linear in Y. 13 00:00:35,630 --> 00:00:39,240 If Y and all of its derivatives are to the first tower. 14 00:00:39,290 --> 00:00:45,150 So again y and all of its derivatives which are the first power and in front of Y in all of its derivatives. 15 00:00:45,320 --> 00:00:48,580 You only have pure functions of x. 16 00:00:48,620 --> 00:00:55,550 Ok so here y and all of these derivatives are to the first power and confront a Y. 17 00:00:55,580 --> 00:00:59,390 And all this derivatives you have pure functions of x all and you should have a pure function of actual 18 00:00:59,400 --> 00:01:00,190 here to. 19 00:01:00,290 --> 00:01:01,290 No problem. 20 00:01:01,310 --> 00:01:02,390 Right so this would be with you 21 00:01:06,450 --> 00:01:07,180 in this case. 22 00:01:07,190 --> 00:01:13,760 Same thing y and all its derivatives are to be first power but it would fail in front of Y in all this 23 00:01:13,760 --> 00:01:16,670 derivatives we have to have pure functions of x right. 24 00:01:16,730 --> 00:01:18,290 You have this little piece here. 25 00:01:18,440 --> 00:01:19,940 This makes it nonlinear. 26 00:01:19,970 --> 00:01:20,210 Right. 27 00:01:20,210 --> 00:01:21,560 We're not allowed to have that right. 28 00:01:21,890 --> 00:01:22,720 That's no good right. 29 00:01:22,730 --> 00:01:23,910 That's not a pure function of x. 30 00:01:23,920 --> 00:01:28,230 The function of y in front of the first derivative that destroys linearity. 31 00:01:28,250 --> 00:01:29,040 This example here. 32 00:01:29,060 --> 00:01:29,870 Why not. 33 00:01:29,890 --> 00:01:33,270 And then all of its derivatives have to appear to the first power fails right away. 34 00:01:33,290 --> 00:01:35,390 You have the first remitted to the fourth power. 35 00:01:35,570 --> 00:01:38,810 So this would be so again. 36 00:01:39,180 --> 00:01:40,820 And it will be linear in Y. 37 00:01:40,820 --> 00:01:45,560 Gentlemen speaking if y and all of its drivers are to the first power and you only have pure functions 38 00:01:45,560 --> 00:01:48,250 of x in front of y and all of its derivatives that's it. 3384