1. Solve the IVP. (xy2 + 3y2)dy-2xdx = 0 y(-4)=-3/18 2. Solve the IVP. y" +2y+2y=8(t- -플) y(0) = 3, y'(0) = = 0 3. Solve the IVP. Answer in explicit form. State the interval of validity for your solution. x dy sin.x +2y = dx x y(2) = 1 4. 5. Use the method of Frobenius about the regular singular point x = 0 to find the indicial roots and recurrence relation for each root. 2xy" +y+y=0 A mass weighing 16 pounds stretches a spring 3 inches. The medium offers a damping force that is numerically equal to 2 times the instantaneous velocity. The mass is released from equilibrium with a downward velocity of 3 inches per second. a. b. Determine the equation of motion. Determine the first time (after t = 0) when the mass first passes through equilibrium. Solve the IVP. 6. y" - 8y' + 15y = 9te² y(0) = −1, y'(0) = 3 7. Find the general solution of the ODE. 8. x²y" 2y 3x² - 1 = x>0 Find the general solution of the ODE. y" +2y-24y: 12x+9-e4x = 9. Solve the IVP. y"" + 12y" + 36y' = 0 y(0) = 0, y'(0) = 1, y"(0) = −7 1
1. Solve the IVP. (xy2 + 3y2)dy-2xdx = 0 y(-4)=-3/18 2. Solve the IVP. y" +2y+2y=8(t- -플) y(0) = 3, y'(0) = = 0 3. Solve the IVP. Answer in explicit form. State the interval of validity for your solution. x dy sin.x +2y = dx x y(2) = 1 4. 5. Use the method of Frobenius about the regular singular point x = 0 to find the indicial roots and recurrence relation for each root. 2xy" +y+y=0 A mass weighing 16 pounds stretches a spring 3 inches. The medium offers a damping force that is numerically equal to 2 times the instantaneous velocity. The mass is released from equilibrium with a downward velocity of 3 inches per second. a. b. Determine the equation of motion. Determine the first time (after t = 0) when the mass first passes through equilibrium. Solve the IVP. 6. y" - 8y' + 15y = 9te² y(0) = −1, y'(0) = 3 7. Find the general solution of the ODE. 8. x²y" 2y 3x² - 1 = x>0 Find the general solution of the ODE. y" +2y-24y: 12x+9-e4x = 9. Solve the IVP. y"" + 12y" + 36y' = 0 y(0) = 0, y'(0) = 1, y"(0) = −7 1
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
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Author:Bruce Crauder, Benny Evans, Alan Noell
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![1. Solve the IVP.
(xy2 + 3y2)dy-2xdx = 0
y(-4)=-3/18
2.
Solve the IVP.
y" +2y+2y=8(t- -플)
y(0) = 3, y'(0) =
= 0
3.
Solve the IVP. Answer in explicit form. State the interval of validity for your
solution.
x
dy
sin.x
+2y
=
dx
x
y(2) = 1
4.
5.
Use the method of Frobenius about the regular singular point x = 0 to find the
indicial roots and recurrence relation for each root.
2xy" +y+y=0
A mass weighing 16 pounds stretches a spring 3 inches. The medium offers a
damping force that is numerically equal to 2 times the instantaneous velocity. The
mass is released from equilibrium with a downward velocity of 3 inches per
second.
a.
b.
Determine the equation of motion.
Determine the first time (after t = 0) when the mass first passes through
equilibrium.
Solve the IVP.
6.
y" - 8y' + 15y = 9te²
y(0) = −1, y'(0) = 3
7. Find the general solution of the ODE.
8.
x²y" 2y 3x² - 1
=
x>0
Find the general solution of the ODE.
y" +2y-24y: 12x+9-e4x
=
9.
Solve the IVP.
y"" + 12y" + 36y' = 0
y(0) = 0, y'(0) = 1, y"(0) = −7
1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbe7e575d-dfd7-411c-ad5f-62e2be64ba9f%2F75be0065-96cc-452f-93b5-7ef1edf20bd7%2Fmahug7d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Solve the IVP.
(xy2 + 3y2)dy-2xdx = 0
y(-4)=-3/18
2.
Solve the IVP.
y" +2y+2y=8(t- -플)
y(0) = 3, y'(0) =
= 0
3.
Solve the IVP. Answer in explicit form. State the interval of validity for your
solution.
x
dy
sin.x
+2y
=
dx
x
y(2) = 1
4.
5.
Use the method of Frobenius about the regular singular point x = 0 to find the
indicial roots and recurrence relation for each root.
2xy" +y+y=0
A mass weighing 16 pounds stretches a spring 3 inches. The medium offers a
damping force that is numerically equal to 2 times the instantaneous velocity. The
mass is released from equilibrium with a downward velocity of 3 inches per
second.
a.
b.
Determine the equation of motion.
Determine the first time (after t = 0) when the mass first passes through
equilibrium.
Solve the IVP.
6.
y" - 8y' + 15y = 9te²
y(0) = −1, y'(0) = 3
7. Find the general solution of the ODE.
8.
x²y" 2y 3x² - 1
=
x>0
Find the general solution of the ODE.
y" +2y-24y: 12x+9-e4x
=
9.
Solve the IVP.
y"" + 12y" + 36y' = 0
y(0) = 0, y'(0) = 1, y"(0) = −7
1
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