53-N5 (0.4 – J0.3)5 + eAxM (1+ /5)" (22– 70°) (4-j179) e/15' + 515 3-N5 (7cls-) - 4+/V5 + [(6j135 – j240)ª (0.4 – J0. 3)°] | X = (2e/m/4 + j-121)2(72-7° + 3eln("/4)³
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- We have shown that in the case of complex conjugate roots,r =a±ib,b̸=0, of the indicial equation, the general solution to the Cauchy-Euler equation y′′+a1y′+a2y =0, x > 0 is y(x)=xa[c1 cos(b ln x)+c2 sin(b ln x)]. .........................(8.8.26) Q. Show that (8.8.26) can be written in the form y(x)= Axa cos(b ln x −φ) for appropriate constants A and φ.Determine whether the Diophantine equation 15x + 53y = 17 is solvable or not.If it is solvable, find its general solution.Find the points of inflection and discuss the concavity of f(x) = 2 cos (3x/2) on (0,2pi)
- Can you also solve for u(t) explicitlySuppose that f(t) = e (1−2i)t is a complex solution for an unknown second-order linear equation ay”+by’+cy = 0, where a, b and c are real numbers. What is the real general solution for the equation? You do not have to compute the Wronskian.Obtain the general solution valid near the origin: 2y" + 9xy' − 36y = 0
- solve by the method of undetermined coefficients. a.) y''-5y=sinx b.) y''+4y=5sin(4x)Evaluate the following: a. L {e3t + cos6t - e3t cos6t} b. L-1 {6s/(s2 + 25) + 3/(s2 + 25)} c. L-1 {se-4s/[(3s + 2)(s - 2)]} Solve: y'' - 6y' + 15y = 2sin3t ; y(0)=-1, y'(0) = -4After many years in business,the financial analyst of a shoe company projected that the monthly costs of producing their products and monthly revenues from the sales of their products are fluctuating according to the following formulas: C(t)=2.6+0.58 sin (0.52t-7.25) R(t)=2.6+1.82 cos(0.52t-7.25) Where C(t) and R(t) are those costs and revenues in million of pesos at month t(t=0 represent January 2010).About how many months after January 2010 did the company experience a zero profit for the first time?