
3. Find the extremals of the functionals (1) (ii) [ Voy (1 + grą) de.
5. Find extremals for the following functionals: (b) J(y) = S. (1 + (y")2) dx, y(0) = 0, y'(0) = 1, y(1) = 1, y(1) = 1.
For the DE 3 (1 — ӕ)(1 — cos Ta ) 3< а <3 Find and classify the equilibrium points
For the DE 3 (1 — ӕ)(1 — cos Ta ) 3
(1) 5 - Yps Sp de - dx to find a second solution of the DE 3. Use the formula ya = yı 9 +2+y = 0, V1 = ce* 4. Find the general solution of each DE.
Let V be a vector space, and ffl, f2, fn) c V be linear functionals on V. Suppose we can find a vector vi e V such that fl (v) 6-0 but £2(v)-6(v) = . . .-m(v) = 0. Similarly, suppose that for all 1 i < n we can find vi є V such that fi(vi) 6-0 and fj (vi)-0 for alljöi. Prove that {fL-fa) is were linearly independent in V ly independent in V * . Prove also...
ii please
b) For the following DE, do the following: a) Find the solution in phase - amplitude form. If we think of each equation as describing a linear mass-spring system, determine how often the mass crosses the equilibrium position. Find the time at which the mass first crosses the equilibrium position. Estimate the time for which «(1< 1/100 i) "+4x'+8x = 0; x(0) = 1; x'(0) = 2 x"+2x'+10 x = 0; x(0) = 1; x'(0) = 1 4x"+4...
help with b please
Homework 10.9. Find extremals for the following functional: b) 5°C2+(3) + 2 ye" .
(b)u=V0 v=0(c)V0
6.6 For the flow defined by the stream function b Voy: (a) Plot the streamlines. (b) Find the a and y components of the velocity at any point. (e) Find the volume flow rate per unit width flowing between the streamlines y 1 and
1 -2 Find the general solution to the homogeneous system of DE: 3 2 6 x' = Ax where A = -2 1 -2
3. [10pts] Consider the DE: xy" + 7xy' + Ty = 0. (a) Find the roots rı and r2 of the indicial equation of the DE (with rı >r2). r = r2 = Solution: (b) If we use Frobenius method to solve the DE, we obtain for the largest indicial root and for n > 0, a recurrence acn relation of the form Cn+1 where a and b are constants. Find a and b. m11
يقوم الانتقال إلى السؤال آخر بحفظ هذا الرد السؤال 1 Determine:- (V1 Voy the BJT amplifier with a=0.988 shown in Figure (1). 55957 4.4668 3,0957 None Figure 1).pdf يقوم الانتقال إلى السوال آخر بحفظ هذا الرد : 13 4.7 kr 604 35kn qure14