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QUESTION 10 dy 2? + 1 If y(x) is the solution of and y(0) = 2 then y(3) = dr y3 OA +2 ОВ. +4 #472 0 OE +22
2 + COS- 2.ry dy d 1+y2 = y(y + sin x), 7(0) = 1. 3. [2cy cos(x+y) - sin x) dx + x2 cos (+²y) dy = 0. 4. Determine the values of the constants r and s such that (x,y) = x'y is an Integrating Factor for the following DE. (2y + 4x^y)dr + (4.6y +32)dy = 0. 2. C = -1 You need to find the solution in implicit form. 3. y = arcsin (C-cos) 4. r=...
dy 22 +1 If y(2) is the solution of and y(0) = 2 then y(3) = da y? II
QUESTION 22 If xyz +z = 15 defines z implicitly as a function of x and y, then 2 dzl дх (2,1,3) O A. 3 8 OB. 0 Ос. 3 OD 4 1 OE. 4
4. (a Let (sin( x cos( ) dr + (x cos(x + y) - 2) dy. dz= Show that dz is an exact differential and determine the corresponding function f(x,y) Hence solve the differential equation = z sin( Cos( y) 2 x cos( y) dy 10] (b) Find the solution of the differential equation d2y dy 2 y e dx dæ2 initial conditions th that satisfi 1 (0) [15] and y(0) 0 4. (a Let (sin( x cos( ) dr...
if y(x) is the solution of dy/dx = (x^(2)+1)/y^(2) y(0)=2 then y(3)=?
Find the solution to the initial value problem: dy dy/dx=x^ 2√1 + x^3/1+cos y y(0)=2 the 1+x^3 is all in square root.
C. This problem is about the inhomogeneous equation dy (1-)2 (1+ x) dy (1-3) (I) y=re +x dr dr2 and the corresponding homogeneous equation dy dy +x dr2 (1- r) (H) -y 0. dr (i) Show that y=r and y= e are solutions of (H). (ii) From (), the general solution of (H) must be y= Ar + Be for arbitrary constants A and B. Solve (I) by the variation of parameters method of Lesson 22, i.e., setting y ur...
Find the solution to the initial value problem dy 6xy + y2 + (3x2 + 2xy + 2y) dx =0 y(1) = 3 OA x+y + 2xy2 + y2 + x = 31 OB. 6xy + 2y2 + x = 37 3x²y + 2x2y + x3 + 2x2 + 2y = 24 OD 3x2y + xy2 + y2 = 27 ОЕ xºy + x2y2 + y2 + x = 22
Select the compounds that are aromatic. Question 1 1 2 3 4 A. 1 and 2 B. 1 and 3 C. 1 and 4 D. 2 and 3 E. 2 and 4 F. 1, 2,4 Enter Your Answer: OA B Ос OD OE OF OK Choose the charged compound(s) that isare) anti-aromatic. Question 2 H 1 2 3 A. 1 only B. 2 only C. 3 only D. 1 and 2 E. 1 and 3 F. 2 and 3 Enter...