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(Solved): Questions #7 - 9: Use separation of variables to obtain the general solution and particular solution ...



Questions #7 - 9: Use separation of variables to obtain the general solution and particular solution to the differential equation

x*cosx=(2y+e^(3y))*y^(')

with the initial condition

y(0)=0

. 7. What is the correct separation of variables? A.

(2y+e^(3y))dx=x*cosxdy

D.

(dx)/((2y+e^(3y)))=(dy)/(x*cosx)

B.

(dx)/(x*cosx)=(dy)/((2y+e^(3y)))

E.

(x-2y)(dy)/(dx)=(e^(3y)-cosx)(dx)/(dy)

C.

x*cosxdx=(2y+e^(3y))dy

8. What is the general solution of the differential equation

x*cosx=(2y+e^(3y))*y^(')

? A.

x*sinx+cosx=y^(2)+(1)/(3)e^(3y)+C

D.

3x^(2)*cosx=(1)/(3)y^(2)+e^(3y)+C

B.

(1)/(2)x^(2)*cosx=y^(2)+3e^(3y)+C

E.

-x*sinx=y^(2)+(1)/(3)e^(3y)+C

C.

-3x^(2)*sinx=(1)/(3)y^(2)+e^(3y)+C

9. What is the particular solution of the differential equation

x*cosx=(2y+e^(3y))*y^(')

with initial condition

y(0)=0

? A.

-3x^(2)*sinx=(1)/(3)y^(2)+e^(3y)+2

D.

x*sinx+cosx=y^(2)+(1)/(3)e^(3y)+(2)/(3)

B.

-x*sinx=y^(2)+(1)/(3)e^(3y)+3

E.

(1)/(2)x^(2)*cosx=y^(2)+3e^(3y)-1

C.

3x^(2)*cosx=(1)/(3)y^(2)+e^(3y)
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