Determine the domain of the function as a solution to the differential equati
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Determine the domain of the function as a solution to the differential equation
Transcribed Image Text:y = 5 tan (5x) is a solution to the
2
Differential equation y₁=25 +y ²
How do I determine the domain of this Solution?
I get IT to // but apparently one of the intervals is 3 IT
10
LO
Expert Solution
Step 1: To find the domain:
As the function y=tan(x) has a domain format('truetype')%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7D%3C%2Fstyle%3E%3C%2Fdefs%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%222.5%22%20x2%3D%2217.5%22%20y1%3D%2220.5%22%20y2%3D%2220.5%22%2F%3E%3Ctext%20font-family%3D%22math1ef1e97aa60a286d0322faa717f%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2210.5%22%20y%3D%2216%22%3E%26%23x3C0%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2210.5%22%20y%3D%2237%22%3E2%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1ef1e97aa60a286d0322faa717f%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2227.5%22%20y%3D%2226%22%3E%2B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20font-style%3D%22italic%22%20text-anchor%3D%22middle%22%20x%3D%2239.5%22%20y%3D%2226%22%3En%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1ef1e97aa60a286d0322faa717f%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2251.5%22%20y%3D%2226%22%3E%26%23x3C0%3B%3C%2Ftext%3E%3C%2Fsvg%3E)
, one may assume the question is concern only in format('truetype')%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7D%3C%2Fstyle%3E%3C%2Fdefs%3E%3Ctext%20font-family%3D%22math13bd038e92a4bc5f3dd3c3a752b%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%226.5%22%20y%3D%2226%22%3E%26%23x2212%3B%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2215.5%22%20x2%3D%2230.5%22%20y1%3D%2220.5%22%20y2%3D%2220.5%22%2F%3E%3Ctext%20font-family%3D%22math13bd038e92a4bc5f3dd3c3a752b%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2223.5%22%20y%3D%2216%22%3E%26%23x3C0%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2223.5%22%20y%3D%2237%22%3E2%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20font-style%3D%22italic%22%20text-anchor%3D%22middle%22%20x%3D%2239.5%22%20y%3D%2226%22%3Et%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20font-style%3D%22italic%22%20text-anchor%3D%22middle%22%20x%3D%2245.5%22%20y%3D%2226%22%3Eo%3C%2Ftext%3E%3Cline%20stroke%3D%22%23000000%22%20stroke-linecap%3D%22square%22%20stroke-width%3D%221%22%20x1%3D%2253.5%22%20x2%3D%2268.5%22%20y1%3D%2220.5%22%20y2%3D%2220.5%22%2F%3E%3Ctext%20font-family%3D%22math13bd038e92a4bc5f3dd3c3a752b%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2261.5%22%20y%3D%2216%22%3E%26%23x3C0%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2261.5%22%20y%3D%2237%22%3E2%3C%2Ftext%3E%3C%2Fsvg%3E)
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