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hannahkelly3618
18.06.2020 •
Mathematics
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)=Acos2x+Bsin2x,
D. yp(x)=(Ax+B)cos2x+(Cx+D)sin2xyp(x)=(Ax+B)cos2x+(Cx+D)sin2x
E. yp(x)=Axe2x,yp(x)=Axe2x, and
F. yp(x)=e3x(Acos2x+Bsin2x)yp(x)=e3x(Acos2x+Bsin2x)
1. d2ydx2−5dydx+6y=e2xd2ydx2−5dydx+6y=e2x
2. d2ydx2+4y=−3x2+2x+3d2ydx2+4y=−3x2+2x+3
3. y′′+4y′+20y=−3sin2xy″+4y′+20y=−3sin2x
4. y′′−2y′−15y=e3xcos2x
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Ответ:
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
Ответ: