Homework Answers
differential equations Problem 2 Solve y"+y= ſt/2, if 0 <t<6, if t > 6 y(0) =...
differential equations
Problem 2 Solve y"+y= ſt/2, if 0 <t<6, if t > 6 y(0) = 6, 7(0) = 8
h Bessel equation of order p is ty" + ty + (t? - p2 y =...
h Bessel equation of order p is ty" + ty + (t? - p2 y = 0. In this problem assume that p= 2. a) Show that y1 = sint/Vt and y2 = cost/vt are linearly independent solutions for 0 <t<o. b) Use the result from part (a), and the preamble in Exercise 3, to find the general solution of ty" + ty' + (t2 - 1/4)y = 3/2 cost. (o if 0 <t < 12, y(t) = { 2...
' )y" + 6xy = 0 about x。:0. #2.) (15 points) For ( 1-X Find two linearly independent solutions y,(x) and V2(x)...
' )y" + 6xy = 0 about x。:0. #2.) (15 points) For ( 1-X Find two linearly independent solutions y,(x) and V2(x) (that is solve the recurrence relation.) This problem is difficult, so plan your time accordingly
' )y" + 6xy = 0 about x。:0. #2.) (15 points) For ( 1-X Find two linearly independent solutions y,(x) and V2(x) (that is solve the recurrence relation.) This problem is difficult, so plan your time accordingly
2. Use the Laplace Transform to solve the initial value problem y"-3y'+2y=h(t), y(O)=0, y'(0)=0, where h...
2. Use the Laplace Transform to solve the initial value problem y"-3y'+2y=h(t), y(O)=0, y'(0)=0, where h (t) = { 0,0<t<4 2, t>4
Solve y'' +9y = $(t – 6), y(0) = y'(0) = 0 g(t) = for t...
Solve y'' +9y = $(t – 6), y(0) = y'(0) = 0 g(t) = for t < 6 for t > 6
Solve y'' + 4y = $(t – 6), y(0) = y'(0) = 0 g(t) = for...
Solve y'' + 4y = $(t – 6), y(0) = y'(0) = 0 g(t) = for t < 6 fort > 6
Question 2 < > Solve y"' + 4y' + 8y = 0, y(0) = 1, y'(0)...
Question 2 < > Solve y"' + 4y' + 8y = 0, y(0) = 1, y'(0) = 6 g(t) = The behavior of the solutions are: O Steady oscillation O Oscillating with decreasing amplitude o Oscillating with increasing amplitude
y(0 ' diany ty-o レ 4.(15 pts) Suppose gi(t), va(t) are solutions of (1 + t)y" + (sint)y ey 0. Suppose also that n attains a maximum and y/2 attains a minimum, both at the point t 5. Do y1, /...
y(0 ' diany ty-o レ 4.(15 pts) Suppose gi(t), va(t) are solutions of (1 + t)y" + (sint)y ey 0. Suppose also that n attains a maximum and y/2 attains a minimum, both at the point t 5. Do y1, /2 form a fundamental set? Explain.
y(0 ' diany ty-o レ 4.(15 pts) Suppose gi(t), va(t) are solutions of (1 + t)y" + (sint)y ey 0. Suppose also that n attains a maximum and y/2 attains a minimum, both at...
Solve the given integral equation or integro-differential equation for yt). t y't) + (t-vy(v) dv=51, y(0)=0...
Solve the given integral equation or integro-differential equation for yt). t y't) + (t-vy(v) dv=51, y(0)=0 0 y(t) =
Problem 3. Solve the following problems: (a) y+ ty -y-0, y(0)-0, (0) 1. (b) ty"+(1 -2t)-2y0, y(0)...
Peoblem 3: Solve the following problems
Problem 3. Solve the following problems: (a) y+ ty -y-0, y(0)-0, (0) 1. (b) ty"+(1 -2t)-2y0, y(0) 1, y'(0) -2 (c) ty" + (t-1)/-y 0, y(0) 5, lime y(t) 0. t-+00
Problem 3. Solve the following problems: (a) y+ ty -y-0, y(0)-0, (0) 1. (b) ty"+(1 -2t)-2y0, y(0) 1, y'(0) -2 (c) ty" + (t-1)/-y 0, y(0) 5, lime y(t) 0. t-+00
differential equations
Problem 2 Solve y"+y= ſt/2, if 0 <t<6, if t > 6 y(0) = 6, 7(0) = 8
h Bessel equation of order p is ty" + ty + (t? - p2 y = 0. In this problem assume that p= 2. a) Show that y1 = sint/Vt and y2 = cost/vt are linearly independent solutions for 0 <t<o. b) Use the result from part (a), and the preamble in Exercise 3, to find the general solution of ty" + ty' + (t2 - 1/4)y = 3/2 cost. (o if 0 <t < 12, y(t) = { 2...
' )y" + 6xy = 0 about x。:0. #2.) (15 points) For ( 1-X Find two linearly independent solutions y,(x) and V2(x) (that is solve the recurrence relation.) This problem is difficult, so plan your time accordingly
' )y" + 6xy = 0 about x。:0. #2.) (15 points) For ( 1-X Find two linearly independent solutions y,(x) and V2(x) (that is solve the recurrence relation.) This problem is difficult, so plan your time accordingly
2. Use the Laplace Transform to solve the initial value problem y"-3y'+2y=h(t), y(O)=0, y'(0)=0, where h (t) = { 0,0<t<4 2, t>4
Solve y'' +9y = $(t – 6), y(0) = y'(0) = 0 g(t) = for t < 6 for t > 6
Solve y'' + 4y = $(t – 6), y(0) = y'(0) = 0 g(t) = for t < 6 fort > 6
Question 2 < > Solve y"' + 4y' + 8y = 0, y(0) = 1, y'(0) = 6 g(t) = The behavior of the solutions are: O Steady oscillation O Oscillating with decreasing amplitude o Oscillating with increasing amplitude
y(0 ' diany ty-o レ 4.(15 pts) Suppose gi(t), va(t) are solutions of (1 + t)y" + (sint)y ey 0. Suppose also that n attains a maximum and y/2 attains a minimum, both at the point t 5. Do y1, /2 form a fundamental set? Explain.
y(0 ' diany ty-o レ 4.(15 pts) Suppose gi(t), va(t) are solutions of (1 + t)y" + (sint)y ey 0. Suppose also that n attains a maximum and y/2 attains a minimum, both at...
Solve the given integral equation or integro-differential equation for yt). t y't) + (t-vy(v) dv=51, y(0)=0 0 y(t) =
Peoblem 3: Solve the following problems
Problem 3. Solve the following problems: (a) y+ ty -y-0, y(0)-0, (0) 1. (b) ty"+(1 -2t)-2y0, y(0) 1, y'(0) -2 (c) ty" + (t-1)/-y 0, y(0) 5, lime y(t) 0. t-+00
Problem 3. Solve the following problems: (a) y+ ty -y-0, y(0)-0, (0) 1. (b) ty"+(1 -2t)-2y0, y(0) 1, y'(0) -2 (c) ty" + (t-1)/-y 0, y(0) 5, lime y(t) 0. t-+00
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