Match the following guess solutions ypyp for the method of undetermined coefficients with the second-order nonhomogeneous linear equations below. A. yp(x)=Ax2+Bx+Cyp(x)=Ax2+Bx+C,
B. yp(x)=Ae2xyp(x)=Ae2x,
C. yp(x)=Acos2x+Bsin2xyp(x)=Acos⁡2x+Bs in⁡2x,
D. yp(x)=(Ax+B)cos2x+(Cx+D)sin2xyp(x)= (Ax+B)cos⁡2x+(Cx+D)sin⁡2x
E. yp(x)=Axe2x, yp(x)=Axe2x, and
F. yp(x)=e3x(Acos2x+Bsin2x)yp(x)=e3x(A cos⁡2x+Bsin⁡2x)
1. d2ydx2−5dydx+6y=e2xd2ydx2−5dydx+6y= e2x
2. d2ydx2+4y=−3x2+2x+3d2ydx2+4y=−3x2+2 x+3
3. y′′+4y′+20y=−3sin2xy″+4y′+20y=−3sin ⁡2x
4. y′′−2y′−15y=e3xcos2x

Step-by-step explanation:

1 ) Given that

For a non homogeneous part , we assume the particular solution is

2 ) Given that

For a non homogeneous part   , we assume the particular solution is

3 ) Given that

y′′ + 4y′ + 20y = −3sin(2x)

For a non homogeneous part −3sin(2x) , we assume the particular solution is

4 ) Given that

y′′ − 2y′ − 15y = 3xcos(2x)

For a non homogeneous part  3xcos(2x)  , we assume the particular solution is

the cat is blue because the probability of extension towards the prefix of the diameter of the circle could only mathematically equal to the sum of the roots of the carrots from   your garden.

step-by-step explanation: