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Consider the vectors 2.0)(8) = ( = ( ),212)() = FO) (a) Compute the Wronskian of...
Consider the vectors х() 3 (, 1)T х°() — (?, 26)Т. and i) Compute the Wronskian...
Consider the vectors х() 3 (, 1)T х°() — (?, 26)Т. and i) Compute the Wronskian of X1 and X2 at t ii) In what intervals are X1 and X2 linearly independent? iii What conclusion can be drawn about the coefficients in the systems of homogeneous differential equation satisfied by X1 and X2? v) Find this system of equations and verify the conclusions of part iii
Consider the vectors х() 3 (, 1)T х°() — (?, 26)Т. and i) Compute...
Consider the vectors x)t) t2 8t and X(2) (t) 10 (a) Compute the Wronskian of x) andx) (b) In wh...
Consider the vectors x)t) t2 8t and X(2) (t) 10 (a) Compute the Wronskian of x) andx) (b) In what intervals are x'') and X㈢ linearly independent? Enter the intervals in the ascending order Equation Editor Equation Editor Common Ω Matrix Common Ω Matrix sin(a) sec(a) COR(a) asc(a) cos(a) tan(a) )三三) 읊 //d.fu. tan a sec(a) Equation Editor Equation Editor Common Ω Matrix Common Ω Matrix sec(a) esc(a) oot(a) cse(a) d z e) What conclusion can be drawn about coefficients...
(3e-4 -8t +9 Consider the vector-valued functions xi(t) = | (-2+2 + 3t) and 22(t) =...
(3e-4 -8t +9 Consider the vector-valued functions xi(t) = | (-2+2 + 3t) and 22(t) = 3e-4t a. Compute the Wronskian of these two vectors. Wx(t) = (67 – 33t+27)e-4t), b. On which intervals are the vectors linearly independent? If there is more than one interval, enter a comma-separated list of intervals. The vectors are linearly independent on the interval(s): (-infinity,1),(1,4.5),(4.5, infinity), help (intervals). c. Find a matrix P(t) = (Pu(t) P12(t)) so that 21 and 22 are fundamental solutions...
1. Compute the Wronskian for the following functions. Then use the Wronskian to determine whether the...
1. Compute the Wronskian for the following functions. Then use the Wronskian to determine whether the functions are linearly independant or linearly dependant. a) {(tan2x - sec2 x),3 (b) le,e,e) 2. Use variation of parameters to find a general solution to 2y" -4ry 6y3 1 given that y 2 and y2- 3 are linearly independant solutions of the associated homogeneous equation. (Hint: be careful the equations are in the right form.) Find a particular solution for each of the following...
I need help with these! 3. (1 point) a) Compute the general solution of the differential equation y"5 12y" 0 b) Determine the test function Y (t) with the fewest terms to be used to obtain...
I need help with these!
3. (1 point) a) Compute the general solution of the differential equation y"5 12y" 0 b) Determine the test function Y (t) with the fewest terms to be used to obtain a particular solution of the following equation via the method if undetermined coefficients. Do not attempt to determine the coefficients.5y 12y"2 10e-tesin(V3t) Spring 2011) 4. (1 point) Compute the general solution of the following differential equations dz dy dt ii)(1y iv) (z cos(y) +...
5. Consider the system of differential equations regarding x = c(t), y = y(t), and z...
5. Consider the system of differential equations regarding x = c(t), y = y(t), and z = z(t): x' = 211 x + 212 y + 213 2 y = 221 x + 222 y + 223 2 z' = 231 2 + 232 y + 233 z where 211, 212,..., 233 are all real constants. Which of the following options could be a general solution of this system? (a) C C[-] é 2t + C2 eft (b) C-1 137...
[4 Mar (c) Consider the following periodic function, defined as: fO) = 7? - ?, -...
[4 Mar (c) Consider the following periodic function, defined as: fO) = 7? - ?, - <t<T and f(t) = f(t + 27) (0 ) State the period, P. [1 Marks) ( 11) Sketch a graph of f(t). [2 marks] State if f(t) is either even or odd, or neither. (1 Marks) (iv) Which Fourier coefficients are zero and why? [1 Marks) (v) Compute do [2 marks] (vi) Compute the non-zero Fourier coefficients. [5 Marks) (vii) Write down the Fourier...
(graded) Section 3.6: Variation of Parameters ITEMS SUMMARY Try again You have answered 1 out of...
(graded) Section 3.6: Variation of Parameters ITEMS SUMMARY Try again You have answered 1 out of 2 parts correctly. Consider the differential equation: 9ty' - 2t(t +9)y +2(t+9) y = -26, t>0. You can verify that yı = 3t and y2 = 2texp(2t/9) satisfy the corresponding homogeneous equation. a. Compute the Wronskian W between yı and 32- W(t) = b. Apply variation of parameters to find a particular solution. Bre,+2te (*),+22
8. Consider the nonhomogeneous linear system of differential equations 1 1 1 -1 u = -1...
8. Consider the nonhomogeneous linear system of differential equations 1 1 1 -1 u = -1 11 1 1 u-et 1 1 2 3 First of all, find a fundamental matrix and the inverse matrix of the fundamental matrix of the corresponding homogeneous linear system. Then given a particular solution 71 uy(t) = et 1 2 find the general solution of the nonhomogeneous linear system of differential equations. Hint: det(A - \I) = -(1 – 2)?(1+1)
Consider the linear system in three equations and three unknowns: 1) x + 2y + 3z...
Consider the linear system in three equations and three unknowns: 1) x + 2y + 3z = 6, 2) 2x − 5y − z = 5, 3) −x + 3y + z = −2 . (a) First, identify the matrix A and the vectors x and vector b such that A vector x = vector b. (b) Write this system of equations as an augmented matrix system. (c) Row reduce this augmented matrix system to show that there is exactly...
Consider the vectors х() 3 (, 1)T х°() — (?, 26)Т. and i) Compute the Wronskian of X1 and X2 at t ii) In what intervals are X1 and X2 linearly independent? iii What conclusion can be drawn about the coefficients in the systems of homogeneous differential equation satisfied by X1 and X2? v) Find this system of equations and verify the conclusions of part iii
Consider the vectors х() 3 (, 1)T х°() — (?, 26)Т. and i) Compute...
Consider the vectors x)t) t2 8t and X(2) (t) 10 (a) Compute the Wronskian of x) andx) (b) In what intervals are x'') and X㈢ linearly independent? Enter the intervals in the ascending order Equation Editor Equation Editor Common Ω Matrix Common Ω Matrix sin(a) sec(a) COR(a) asc(a) cos(a) tan(a) )三三) 읊 //d.fu. tan a sec(a) Equation Editor Equation Editor Common Ω Matrix Common Ω Matrix sec(a) esc(a) oot(a) cse(a) d z e) What conclusion can be drawn about coefficients...
(3e-4 -8t +9 Consider the vector-valued functions xi(t) = | (-2+2 + 3t) and 22(t) = 3e-4t a. Compute the Wronskian of these two vectors. Wx(t) = (67 – 33t+27)e-4t), b. On which intervals are the vectors linearly independent? If there is more than one interval, enter a comma-separated list of intervals. The vectors are linearly independent on the interval(s): (-infinity,1),(1,4.5),(4.5, infinity), help (intervals). c. Find a matrix P(t) = (Pu(t) P12(t)) so that 21 and 22 are fundamental solutions...
1. Compute the Wronskian for the following functions. Then use the Wronskian to determine whether the functions are linearly independant or linearly dependant. a) {(tan2x - sec2 x),3 (b) le,e,e) 2. Use variation of parameters to find a general solution to 2y" -4ry 6y3 1 given that y 2 and y2- 3 are linearly independant solutions of the associated homogeneous equation. (Hint: be careful the equations are in the right form.) Find a particular solution for each of the following...
I need help with these!
3. (1 point) a) Compute the general solution of the differential equation y"5 12y" 0 b) Determine the test function Y (t) with the fewest terms to be used to obtain a particular solution of the following equation via the method if undetermined coefficients. Do not attempt to determine the coefficients.5y 12y"2 10e-tesin(V3t) Spring 2011) 4. (1 point) Compute the general solution of the following differential equations dz dy dt ii)(1y iv) (z cos(y) +...
5. Consider the system of differential equations regarding x = c(t), y = y(t), and z = z(t): x' = 211 x + 212 y + 213 2 y = 221 x + 222 y + 223 2 z' = 231 2 + 232 y + 233 z where 211, 212,..., 233 are all real constants. Which of the following options could be a general solution of this system? (a) C C[-] é 2t + C2 eft (b) C-1 137...
[4 Mar (c) Consider the following periodic function, defined as: fO) = 7? - ?, - <t<T and f(t) = f(t + 27) (0 ) State the period, P. [1 Marks) ( 11) Sketch a graph of f(t). [2 marks] State if f(t) is either even or odd, or neither. (1 Marks) (iv) Which Fourier coefficients are zero and why? [1 Marks) (v) Compute do [2 marks] (vi) Compute the non-zero Fourier coefficients. [5 Marks) (vii) Write down the Fourier...
(graded) Section 3.6: Variation of Parameters ITEMS SUMMARY Try again You have answered 1 out of 2 parts correctly. Consider the differential equation: 9ty' - 2t(t +9)y +2(t+9) y = -26, t>0. You can verify that yı = 3t and y2 = 2texp(2t/9) satisfy the corresponding homogeneous equation. a. Compute the Wronskian W between yı and 32- W(t) = b. Apply variation of parameters to find a particular solution. Bre,+2te (*),+22
8. Consider the nonhomogeneous linear system of differential equations 1 1 1 -1 u = -1 11 1 1 u-et 1 1 2 3 First of all, find a fundamental matrix and the inverse matrix of the fundamental matrix of the corresponding homogeneous linear system. Then given a particular solution 71 uy(t) = et 1 2 find the general solution of the nonhomogeneous linear system of differential equations. Hint: det(A - \I) = -(1 – 2)?(1+1)
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