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Consider the equation
x2y′′+ xy′- y = 4x ln x
(a) Verify that x is a solution to the homogeneous equation.
(b) Use the method of reduction of order to derive the second solution to the homogeneous equation as Cx-1
(c) Use the method of variation of parameters to show that the general solution of the equation can be written as
y = x(ln x)2- x ln x + c1x + c2x-1
y=x4/4lnx-x4/16 then dy/dx=? Solution) dy/dx=-x^3/4(2/lnx-1)^2. ^ means power
Evaluate following integrals. (a) ∫ 3e x + 5 cos x -10 sec 2 x dx (b) ( 23/ (y 2 + 1) + 6 csc y cot y + 9/ y dy Solution (a) ∫ 3e x + 5 cos x -10 sec 2 x
Question: Solve the initial value problem 2x'' +x'-x =27 Cos2t +6 Sin 2t, x(0)=2 , x'(0)= -2 by using Laplace transform method.
The sum of the square of a number and 12 times the number is -27. What is the smaller probable value of this number? Let x = the number. The statement that is "The sum of the
1. The polynomial G(x) = -0.006x4 + 0.140x3 - 0.53x2 + 1.79x measures the concentration of a dye in the bloodstream x seconds after it is injected. Does the concentration increase
into how many smaller part is each centimeter divided
Prove that A tree with n vertices has (n - 1) edges. Ans: From the definition of a tree a root comprise indegree zero and all other nodes comprise indegree one. There should
a statisics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 46.0 and 56.0 minutes. find the probability that a given class pe
Find the sum of all natural numbers amongst first one thousand numbers which are neither divisible 2 or by 5 Ans: Sum of all natural numbers in first 1000 integers which ar
Mark intends to tile a kitchen floor, which is 9 by 11 ft. How many 6-inch tiles are required to tile the floor? a. 60 b. 99 c. 396 c. Since the tiles are calculated in
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