Need Help with Practice Exam Short Answer Questions, Differential Equations
Need Help with Practice Exam Short Answer Questions, Differential Equations (1 if (<t<1 3. If fz(t)...
This is a differential equations course. Please answer all questions. Find the general solution Problem 1 Find the general solution 1. ༧(༩) = ( 2) -t (0 2. r (t) = [1 1 0 1|z(4) 1 (0) 3. ༧(༩) = (I i) -(8) ) = ( 2+) •(4) 4. z(t) = 1 5. z(t) = [1 2 12 2 11=(2) 1 1 6. +(t) = 1 2 =5 1 1 = 1 -11+(t) =9 ) - 324 2 0 2]...
(4) (a) Compute the Fourier series for the function f(x) interval [-π, π]. 1-z on the (b) Compute the solution u(t, z) for the partial differential equation on the interval [0, T): 16ut = uzz with u(t, 0)-u(t, 1) 0 for t>0 (boundary conditions) (0,) 3 sin(2a) 5 sin(5x) +sin(6x). for 0 K <1 (initial conditions) (20 points) Remember to show your work. Good luck. (4) (a) Compute the Fourier series for the function f(x) interval [-π, π]. 1-z on...
This is a differential equations course, please answer all the questions. Find the general solution. 1 - 1 8. I'(t) = 3 3 2 2 1 -1 (t) 3 2 -2 9. z'(t) -2)=(1) 10. 2'(7) = (1 -1)=(0) 11. z'(t) 2(t) =) =(0) 13. zº(t) = 6 (5 -3) =(0) 14. 2°(8) = (1, -1)=(0) 12. z'(t) = ON DINE 1 0 0 15. x'(t) = 21 2 1 -2 (t) 3 2 -1 16. :'(t) = -3 1...
3. Consider the differential equation ty" - (t+1)yy = te2, t> 0. ert is a solution to the corresponding homogeneous (a) Find a value of r for which y = differential equation (b) Use Reduction of Order to find a second, linearly independent, solution to the correspond- ing homogeneous differential equation
find the general solution for 6,7,8 (differential equation) 6. L'(t) = 1 1 -1 r(t) -3 -8 -5 3 2 4 7. :'(t) = 2 0 2 r(t) 4 2 3 1 8. r'(t) = 3 2 -1 2 1 4 -1 (t) Recall: Given two functions f(t) and g(t), which are differentiable on an interval I, • If the Wronskian W(8,9)(to) #0 for some to El, then f and g are linearly independent for all t E I. If...
need help with these questions as soon as possible PROBLEM 3: Simplify the following expressions (to review the properties of the unit impulse): a. f(t 5)6(t -5) etn dt PROBLEM 4: Mathematical Review Problem 1.54(a, b, d) PROBLEM 5: a) Consider the signal t) defined below 0, t<0 n(t) = t<2 t, 0, 1 t2 2 Write a single equation for xi(t) using the unit step function (i.e. do not use bracket notation). b) Sketch the signal z2(t) = u(t...
Problem 3: Insights into Differential Equations a. Consider the differential equation 습 +4 = f(t), where f(t) = e-u, 12 0. Please write the forms of the natural and forced solution for this differential equation. You DO NOT need to solve. (7 points) b. Again consider the differential equation f(t), where f(t) is an input and y(t) is the output (response) of interest. Please write the differential equation in state-space form. (10 points) c. The classical method for solving differential...
This is a differential equations course, please answer all the questions. Find the general solution. 1 1 6. x'(t) = 1 2 -8 -1 :(t) 1 -5 -3 3 2 4 7. z'(t) = 2 0 2 *(t) 4 2 3 1 -1 2 8. :'(t) 2 11. I't) 3.-0 9. z'(t) = (3 =) =(8) 10. z'(t) = (1' -1)=() = ({ -2)=(6) -1)=(0) -3)=66 14. z'(t) = (-; -1)=() 2)- 12. z't) 13. :') 5 15. z'(t) =...
DIFFERENTIAL EQUATIONS Solutions of Systems of Linear Differential Equations (L01.5 - 15 points) Show that the general solution of the nonhomogeneous linear system is x=(1 71}x+ []}<+[4.]e + 3' X=al_2-vzlevat +al-1 + vale-vēt + [1]{2+{2}]++ [4]
Linear Algebra! Practice exam #1 question 1 Thanks for sloving! 1- Transformations (3 points each) a) Given a linear transformation T :N" N" T(x,y)-(x-y,x+y) and B= {< l, 0>.< 1,1 >} , B = {< l, l>,< 0, l>} V,-< 2, l> Find V,T,and TVg) b) Given a linear transformation T:n'->n2 T(x,y,2)-(x-z,x +2y)and V =< 2,-I, I> B= {<l, 0, 1>.< 1, 1, 0 >, < 0, l, 0 >}, B' = {<l, l >, < 0, 1 >} Find...