Math Problem Statement
There is a system where Ax=B and A=[-1,2,3,6;0,1,-3,2;4,6,5,0;9,-2,-3,4] and x = [x1;x2;x3;x4] and B=[3;4;-2;-1]. There is also a given function: arcctg(sqrt(x))+(sqrt(4+x^2))^3 *y+2+sqrt(x)+cos(x)-(x^2 +1)*y = ln(1+sqrt(x)). Write in an open way y=y(x) and calculate the value of the function y(x4). Provide the answer with four decimal places.
Solution
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Trigonometry
Logarithms
Nonlinear Equations
Formulas
Matrix equation A · x = B
arcctg(sqrt(x)) + (sqrt(4+x^2))^3 * y + 2 + sqrt(x) + cos(x) - (x^2 +1) * y = ln(1 + sqrt(x))
Theorems
Inverse Matrix Method or Gaussian Elimination (for solving Ax = B)
Properties of Logarithms and Trigonometric Functions
Suitable Grade Level
Grades 11-12 or early college level
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