2. Solve the IVP. y" +y= g(t) y(0) = 0, y'(0) = 1 t 0≤t<1 g(t) = 1 t≥ 1 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. Solve the ODE. 5. dy y dx = (2x-3)(2-1) 2(x-2)(x-1) 6. Find the general solution of the ODE. y"-6y' +9y=x-³ ³x 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" + 4y = 3 sin(2x)
2. Solve the IVP. y" +y= g(t) y(0) = 0, y'(0) = 1 t 0≤t<1 g(t) = 1 t≥ 1 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. Solve the ODE. 5. dy y dx = (2x-3)(2-1) 2(x-2)(x-1) 6. Find the general solution of the ODE. y"-6y' +9y=x-³ ³x 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" + 4y = 3 sin(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:2.
Solve the IVP.
y"
+y= g(t)
y(0) = 0, y'(0) = 1
t 0≤t<1
g(t)
=
1
t≥ 1
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.
Solve the ODE.
5.
dy
y dx
=
(2x-3)(2-1)
2(x-2)(x-1)
6. Find the general solution of the ODE.
y"-6y' +9y=x-³ ³x
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" + 4y = 3 sin(2x)
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