Question 5 5. Find the general solution using variation of parameters Y" - y'- 2y 2. an -t
2 +2y - 2=3, I-y=2, 2.0 + y - 2= 5. 1. Write the system as an augmented matrix and perform some elementary row operations to make it in row reduced row echelon form. 2. What is the rank of the augmented matrix? How many free variables does this system have. 3. Write the solutions of the system in parametric form. 4. Consider the following system 2 + 2y - 2=3, r-y=2, 2.x + y -2=1. (The only difference is...
2y + y + 2y = g(t), (O) = 0, y'(0) = 0 where g) 5 St<20 10, 0<t<5 and t > 20
completeness and clarity 2. Find a particular solution for the IVP y" - 2y + 2y = 8(t - 5), y(0) = 0, y0) = 1
1. Solve the following differential equations: a. xy'=y+Vxy x+2y+3 y'= b. 2x – y +5 x+2y+3 y'= x+2y+5 y cos(x+y)+x+y d. sin(x + y) + y cos(x+y)+x+y C. y'=
5. 2 cos x cos y= cos(x+y) + cos (x-y) 6. sin2x + sin 2y = 2 sin(x+y)cos(x-y)
6. Use the 1st shifting theorem 5. Y"-34 +2y = 2 to solve te at y + 4y + 4y y (0)=0, 4 (0) = 1 theorems to compute hifting
find maximum value with steepest ascent method of f(x,y)=5+2xy+2y-x^2-2y^2 by: a)program code(any but matlab is preferred) b)without program code Do 3times of iteration with initial guess is (x,y)=(0.25,0.25)
3. Solve differential equation by undetermined coefficient methods y" + 2y' +2y = 5 3 4. Solve differential equation by undetermined coefficient methods 1 + 6y +8y = 3 - 2 + 2.
2y - 1 E Evaluate by + 2 if possible, for a) y = 2 and b) y = -4. Express answers as integers or simplified fractions, if necessary. 2y - 1 a) For y = 2, the expression 6y + 2 is b) For y = -4, the expression 2y - 1 6y + 2 is