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

.there can be infinite values of m and n that can satisfy the above equation. for each value of m of m or n. there maybe infinite sets of solution for the above

step-by-step explanation:

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.