Find a power series solution for the following differential equations.

The differential equation \(x^{2} y^{\prime \prime}+x y^{\prime}+\left(x^{2}-1\right) y=0\) is a Bessel equation of order 1. Use a power series of the form.

Text Transcription:

x^{2} y^{\prime \prime}+x y^{\prime}+\left(x^{2}-1\right) y=0

Courtney C. Module 2 Biology 530 abnormal bone growth gigantism and dwarfism is an excess or deficiency of growth hormone during normal growth period acromegaly is when bones become thicker due to GH induced apositional growth excess growth hormone after normal growth period Human growth hormone has an effect on bone length and mass during the years leading to adulthood. Human growth hormone is described by some as the key to slowing the aging process. Before you sign up, get the facts — and understand proven ways to promote healthy aging. Growth hormone levels throughout the life of an individual vary. It is at its highest level during the growth spurt of the teen age years. There is little evidence that taking growth hormone as an adult actually slows the aging process and may do harm. Growth hormone, produced by cells in the anterior pituitary, is a major factor in causing and maintaining the proliferation of cartilage cells in the epiphysis of bones that are growing longer. . During the growth and development of childhood to early adult life, if there is too little of this hormone available, then individuals will be shorter to the extreme case of a dwarf; if too much and over a longer than normal period of time, then individuals will be unusually tall (gigantism). During adult life, after the epiphyses have closed, if excess growth hormone is produced, then bones will grow by the only method that they can a