00:01
Question number 18, d square y over d x square is equal to 3 into sine x minus 4y.
00:20
So, d square y over d x square plus 4y is equal to 3 sinex.
00:33
M square plus 4 is equal to 0.
00:37
So m is equal to plus minus iota 2.
00:45
Hence y is equal to a cos of 2x plus b sine of 2x now let y is equal to c cause x plus d sine x so d y over d x is equal to minus c sine x plus d cause x and d sky over d x square is equal to minus c cause x minus d sine x hence the equation becomes minus c cause x minus d sinex plus four c cause x plus 4d sine x is equal to 3 sine x so the simplified form equation would become 3c cause x plus 3d sine x is equal to 3 sine x so comparing the equation value of c is equal to 0 d is equal to 1 so, y is equal to sine of x.
02:34
From here, general equation would become y is equal to a cause of 2x plus b, sine of 2x plus sine x.
02:55
Y is equal to 0 when x is equal to 0.
03:01
So, a is equal to 0.
03:04
D .y over d x is equal to 1, when x is equal to pi by two so d y over d x is equal to minus two a now d y over d x is equal to minus two a sign of two x plus two b cause of two x plus cause of x so from here b is equal to minus 1 over 2...