dy If y(x) is the solution of dr 22 +1 and y(0) = 2 then y(3) = 33 OA +2 OB. +2V2 ос 0 OD +4 OE +4V2
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=...
if y(x) is the solution of dy/dx = (x^(2)+1)/y^(2) y(0)=2 then y(3)=?
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...
dy 22 +1 If y(2) is the solution of and y(0) = 2 then y(3) = da y? II
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...
Q1: Solve the ODE: f) Vyy' + y3/2-1. y(1) = 0. g) (2x +y)dx(2x+y-1)dy 0. i) dx=xy2e": y(2)=0. j) (1 + x*)dy + (1 + y*)dx = 0; y(1) = V3. Q1: Solve the ODE: f) Vyy' + y3/2-1. y(1) = 0. g) (2x +y)dx(2x+y-1)dy 0. i) dx=xy2e": y(2)=0. j) (1 + x*)dy + (1 + y*)dx = 0; y(1) = V3.
The phase plot for an ODE dy dx =f(y) dydx=f(y) is shown below. 4 3 2 1 2 1 1 1 1 2 3 (a) Which of these could be a plot of solutions y vs x corresponding to this ODE? 9 2 B. A. 2 2 3 C. D. You can click the graphs above to enlarge them. OA. A ов, в OC. C OD. D E which is choose (b) The smallest equilibrium of this ODE is y-...
QUESTION 20 sin? y cos’ y dy= 0 ОА. #/16 ОВ. · 91/4 Ос. 1 OD 0 E. 9/2