Question

7. Solve the differential equation: x x + (ax – 7)y = bx? (Note: Where a and b are any two numbers of your MEC ID No. and a, b>0) (9 marks)

a=1    b=3

Answer 1

For This differential equations we cannot solve exactly ,we solve as an approximate solution

ndy + (an-7)y= but riven that a=2, 6=3 Can be written as dy + (0-7) y =327 + compairing where 3 + (1-4) +- 3x + ♡ with dy + py=gin) P=1-7 Thuis The Integrating factor is Il-7 da n-flon e се -Flan =en ie =en fector, multiplying ③ by Integrating 27 nt Int zen X Folgen 27 en fa 214 at se on the no- Hydx dy -Ey dr = Bei den d(yeny) = 3en da integrating both Side yen = Jan de + c Constent

Note we can be extend our solution ens 1+ + + zem - 3[++++ ] --) 3.13 Integrating both side S = 3 [lnntatem 2 L2 na) =3 lant 3 Ž 22 = 3 enn + È an S sen na, non The solution is y= 2 2 [ 13ch dat ] where J3ch = = 3 lax +3 En. hal