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Exact Differential Equations. Let y(x) be the solution of the following initial value problem: (cos z...
exact differential equations 2. Solve the initial value problem: (2.1 – y) + (2y – r)y' = 0) with y(1) = 3. 3. Find the numerical value of b that makes the following differential equation exact. Then solve the differential equation using that value of b. (xy? + br’y) + (x + y)x+y = 0
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...
1. (10pts) Find the solution to the initial value problem for the following differential equations 1/' + 2y - 8y = (2x + 2?), y(0) = -1, 7(0) = 0.
differential equations 2. (a) Verify that yı = e cos x and y2 = etsin x are solutions of -2y + 2yło on (-00,00). 204 Chapter 5 Linear Second Order Equations (b) Verify that ifc, and are arbitrary constants then y = cre* cos x + cze sinx is a solution of (A) on (-00,00) (c) Solve the initial value problem y" - 2y + 2y = 0, y(0) = 3. y'(O) = -2
could you answer all questions 14. Solve the initial-value problem for the exact ordinary differential equation. 2ry-9+(2y + 2 +1)y-0, y (0) --3 OAy- r O B. y O C. y O D. y O E. y OF.y O G. y rT VZS122E25 15. Solve the initial-value problem for the exact ordinary differential equation. 2ry-9r2 +(2y + x2+1)y-0, v(0) 2. -1+V12r2125 21 OA.y t B. y nren OC.y= e OD. y ra OE. y lag OFy= G. y ipprypr 1+v...
Question 1: (20 points) Find the solution of the initial value problem a = cos? x – sin x – 2y cos x + y2 , y(0) = given that yi(2) = cos x is a solution of the differential equation.
The solution of the Initial-Value Problem (IVP) z? yll – 2y = 4(x - 2) y(1) = 4 y (1) = -1 is . 4 y == + x2 - 2x + 1 2 None of them 0 1 O y = +22 - 2x + 4 2 O y = 1 +73 - 2x + 4 22 O v= +222+3
non-homo 2nd order linear equations 1. Find the general solution for each of the following differential equations (10 points each): (a) (b) (e) y" – 2y! - 3y = 3e2x y" — y' – 2y = -2.3 + 4.2? y" + y’ – 67 = 1234 + 12e-2x y" – 2y' – 3y = 3.ce-1 y" + 2y' + y = 2e- (Hint: you'll use Rule 7. at least once) (e 2. Find the solution to the following differential equation...
6. Solve the initial value problem y" + y = 0, y(0)=0, y'0=1 (a) -COS X (b) -sin x (c) -sin x + cos x (d) -sin x COS X (e) COS X (f) sin x (g) sin x-COS X (h) sin x + cos x 7. Find a particular solution yn of the differential equation (using the method of undetermined coefficients): y + y =p2 (a) 2e (b) 3e (c) 4e: (d) 6e (e) 2/2 (f) e2/3 (g) e2/4...
c. exact with solution ZXY+y+C d. exact with solution 2xy +y=c e. not exact lemy 8. The solution of (x +2y )dx + ydy = 0 is a. Inx+ln(y+x)=C b. 1((v+x)/x)=C c. 1(y+x)+x/(x+x)=C d. In(y+x)+x/(y+x) +c e. it cannot be solved