Here y' = dy/dx
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Pre-class exercise 1. Verify that -3x y=C e 3x is a solution to y'=-3y.
Use undetermined coefficients to find the particular solution to y’’ – 4y' + 3y = e*((22 – 122 )cos(3x) + (58 + 362 )sin(3x)) Yp(x) = Preview
2. x+4y= 14 2x - y=1 x=2, y=3 3. 5x + 3y = 1 3x + 4y = -6 x=2, y=-3 | 4, 2y- 6x =7 3x - y=9 No solution/Parallel lines
Consider the field {m{x,y],n[x,y]} given by: [1+3x-3x^2 +3y^2, -3y +6xy} Could this field be a candidate for a model for of a fluid flow without sources or sinks? What is the flow of this field along the ellipse ((x-3)^2/2^2) + 6(y+2)^2=1
5. (5 points) a) Find a particular solution of y" +3y+4y 3x+2. b) Determine the appropriate form for a particular solution of y-4y- 2e* (2 points)
. Consider the IVP: y + 3y = e 3t, y(0) = 1, y(0) = 0 - Solve the IVP using the guess and test method. .Solve the IVP using the general formula for integrating factors. - Solve the IVP using Laplace Transforms. . Verify that your solution satisfies the differential equation (you should get the same solution using Il three methods, so you only need to test it once).
Find the general solution for the differential equation. x dy/dx + 3y = 4x2 – 3x; x>0 y=_______
2. Consider the homogeneous equation r2y"- (3r2 2x)y (3x + 2)y= 0. (a) Verify that y = x is a solution to the homogeneous equation. (b) Use reduction of order to find the general solution.
Use the transformation u = 3x + y, v=x + 3y to evaluate the given integral for the region R bounded by the lines y = - 3x + 1, y= - 3x + 3, y= - = X, and y=- -x + 2. ne lines y = – 3x+1, y = – 3x+3, y=-3x, and y=-**+2. 3 Siſ(3?+ 16 +3%) dx ay SJ (3x? + 10x9 +35) dx dy=0 (Simplify your answer.)
2.) Let Z the set of integers and two binary operations on it: Z23(x,y) → xTy = xy + 3x +3y +6 e Z i) Show (Z,L,T)is an integral domain ii) Find the set of units U(Z)
2.) Let Z the set of integers and two binary operations on it: Z23(x,y) → xTy = xy + 3x +3y +6 e Z i) Show (Z,L,T)is an integral domain ii) Find the set of units U(Z)
3. Solve the system of differential equations X'= 3x+y y = x+3y