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If a second-order differential equation has a characteristic equation with complex conjugate roots of the form r 1 = a + bi and r 2 = a − bi, then the general solution is accordingly y(x) = c 1 e (a + bi )x + c 2 e (a − bi )x. By Euler's formula, which states that e iθ = cos θ + i sin θ, this solution can be rewritten as follows:
Answer: B.) Hippopotamus. 5th Grade Level Questions. 21. What is the subordinating conjunction in the following sentence? “They lost the competition because they didn’t practice.” Answer ...
Hosted by comedian Jeff Foxworthy, the original show asked adult contestants to answer questions typically found in elementary school quizzes with the help of actual fifth-graders as teammates ...
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
Characteristic equation may refer to: Characteristic equation (calculus), used to solve linear differential equations; Characteristic equation, the equation obtained by equating to zero the characteristic polynomial of a matrix or of a linear mapping; Method of characteristics, a technique for solving partial differential equations
The characteristic of a ring R is the natural number n such that n is the kernel of the unique ring homomorphism from to R. [a]The characteristic is the natural number n such that R contains a subring isomorphic to the factor ring /, which is the image of the above homomorphism.