y" + X²y = Σ ak sin(kët), 0 < λ ‡ kπ,\k € {1, ..., N}. k=1
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- multiple s(x, y.:) - Ax*e" - Bz'cos(r*y' )+ Cx*y°z*, where the coefficients 4.B.C, 1. Given the variable function are the last three digits of your index number, calculate:- af i) af ii) dy af iii) dzQ3) A: Find y if: a- y = sin 2x + 2 cos x c- y = sin √x (As... b- y = secx. csc x d- y tan(2x + 1)If C is a circle of radius 6 centered at the point (3, -1), then evaluate f (4y – e³in (2)) dx + (10x − sin(y³ + y))dy. - - value = π
- G) = 2 3. (sin x)y' + y cos x = x sin x, (4pts)4) Find dy given: y (1-x)(1+xX1+x³X1+x*) dx 5) Find dx given: y= (5x² - 3(7x° + x)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
- 4. Find d?y/dx2 for the following functions: a) y = sin x2 cos 2x b) y = cos (sec2 3x) c) y = x²(x3 – 1)5 -1 d) y = (1- x/2) 1 O O DFind the form for a particular solution to the equation y "+2y'– 3y =r?cos (nt). A (a,+a,²+a,t+a,)cos(xt) B - a t+a) cos (at) © (a,12+a,1+a,)² cos (xt) D(a,r²+a,t+a) cos(xt) +1(b,t²+b,t+b,) sin (xt) E (a,r²+a,t+a) cos (t) + (b,ť²+ b,t+b,) sin ( xt)Solve all numbers
- 2.as qucik as possible pretty pleaseSolve one of the following deferential equations a) rsine de + (r³2r² cose + cose)dr = 0. b) (xy + y)dx + 2(x² y² +x+y)dy = 0u =x² +y² +=', x=e" cos 21, y =e21, := e = =? O a e" (cos 21 – sin 41 + 8t +8t)+2e*" Ob. e" (cos 21 - 2sin 41 + 8t +16r) +2e e (cos 21-2cos 21 +4t+& +2) d. e (sin 21-2 sin 2t +4t+16r +2) Oe. e" (sin 21-2 sin 4f)+e (4t+16r +2)