= 0 Siny 54+3x dx dy 7712 (5xy+3x3 2 0 д 12 Smy dy 5ysing + 3 siny 2 dy 7712 3 sin2y = -5y cosy +5 smy 3 y. 8 7/2 = - 5y cosy + 5 siny + 3 y 3 sin 2y 4 8 0 = -5 I cos I II cos I + 5 sin+ 3хд 2 3 Sin 2 (2) m2(즐) 8 - (-5) -5x ox cos + 55100) + 10 ΧΟ 8 = 5+38 Ans

Find dy/dx

Find ds/dt if 3t + 3s sin(3t) + 3cos(t) %3D

Find :y``+ 2y` + y = cos²xturn to1-cos2x/2

11. Evaluate * d²y dy 2. + 5y = –17sin2x - dx² dx y = (C,e* + 68 cos2x + (Cze* + sin2x 15 y = (Cze* + 4)cos2x + (Cze* + 1)stn2x 15 А. В. 153 y = (C,e* + 68 cos2x + (Cze* + y = (Ce* – 4)cos2x + (Cze – 1)stn2x 97 sin2x 97 O D.

dz Find , if z = cos(3x² + 7y) O 2x sin(3x² + 7y³) sin(3x? + 7y') -9x cos(3x2 + 7y°) -6x sin(3x? + 7y°)

If x*y" + xy' + (x? -)y=D x >0 ,V1=x 2sinx and y = y,v. Which of the following equations satisfied by v Select one: a. (x 2 sinx)v" + (2x 2 cosx)v' = 0 b. (x 2sinx)v" +(2x 2 cosx)v=0 C. (x2sinx)v" + (2x cosx – xsinx + x2 sinx)v' = 0 cosx - x 2 sinx + x 2 sinx)v' = 0 d. (x 2 sinx)v" +(2x2 cosx)v' =0

Show complete solution 7-9

5) 3tan-1x + sin-1x = 4 X.

جواب عمومی معادله دیفرانسيل fcamul plas (2xy sin²x)y' + x³ + xy² sin 2x + y²sin²x = 0 x+ .a * cos 2x + cos 2x + 4 = C 4 - 2 .b xy²sin?x + 4 | .c xy sin 2x + = C - 4 .d -y² cos²x+ y² cos 2x + 4 = C 4 -