3. 4. Write the general solution of the ODE by finding two power series solutions about the ordinary point x = 0. Write out the first 3 nonzero terms in each series. (x2+1)y" + xy-y=0 Find the charge on the capacitor in an LRC-series circuit if L = 1 henry, R = 4 ohms, C=0.2 farad, and E(t) = 120 volts. The initial charge and the initial current are both zero. 5. Solve the ODE. dy (2x-3)(y² - 1) y = dx 6. 2(x-2)(x-1) Find the general solution of the ODE. y"-6y+9y=x-33x 7. Find the general solution of the ODE on (0,∞). 8. 9. x²y" - xy + y = 2x Solve the IVP. Answer in explicit form. State the interval of validity for your solution. dy dx x(x+1) +xy = 1 y(e) = 1 Find the general solution of the ODE. y"+4y3sin(2x)
3. 4. Write the general solution of the ODE by finding two power series solutions about the ordinary point x = 0. Write out the first 3 nonzero terms in each series. (x2+1)y" + xy-y=0 Find the charge on the capacitor in an LRC-series circuit if L = 1 henry, R = 4 ohms, C=0.2 farad, and E(t) = 120 volts. The initial charge and the initial current are both zero. 5. Solve the ODE. dy (2x-3)(y² - 1) y = dx 6. 2(x-2)(x-1) Find the general solution of the ODE. y"-6y+9y=x-33x 7. Find the general solution of the ODE on (0,∞). 8. 9. x²y" - xy + y = 2x Solve the IVP. Answer in explicit form. State the interval of validity for your solution. dy dx x(x+1) +xy = 1 y(e) = 1 Find the general solution of the ODE. y"+4y3sin(2x)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:3.
4.
Write the general solution of the ODE by finding two power series solutions about
the ordinary point x = 0. Write out the first 3 nonzero terms in each series.
(x2+1)y" + xy-y=0
Find the charge on the capacitor in an LRC-series circuit if L = 1 henry, R = 4
ohms, C=0.2 farad, and E(t) = 120 volts. The initial charge and the initial current
are both zero.
5.
Solve the ODE.
dy
(2x-3)(y² - 1)
y
=
dx
6.
2(x-2)(x-1)
Find the general solution of the ODE.
y"-6y+9y=x-33x
7.
Find the general solution of the ODE on (0,∞).
8.
9.
x²y" - xy + y = 2x
Solve the IVP. Answer in explicit form. State the interval of validity for your
solution.
dy
dx
x(x+1) +xy = 1
y(e) = 1
Find the general solution of the ODE.
y"+4y3sin(2x)
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