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Verification For each differential equation, verify by differen. tiation and substitution that the given function is a solution. 1. y = y² +4 (1|4): y = 2 tan 2r

Verification For each differential equation, verify by differen. tiation and substitution that the given function is a solution. 1. y = y² +4 (1|4): y = 2 tan 2r

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
For each differential equation, verify by differentiation and substitution that the given function y is a solution. a. y' = (y ^2) + 4 (|t|0) y = (t^2)*In(t)Verification For each differential equation, verify by differentiation and substitution that the given function is a solution. 2 y = y² +4₁ (ltl) < (7); 4 1 , y = 2tan 2t y = -y+t(t) > (0): ² y + 2 ,y = 3t+t y = 2y + 1(t) > (0); t t. -2(s² - t²) 2 ‚y = t_ Inty - 4ty = 1:,y = Se 0 ds
Transcribed Image Text:For each differential equation, verify by differentiation and substitution that the given function y is a solution. a. y' = (y ^2) + 4 (|t|0) y = (t^2)*In(t)Verification For each differential equation, verify by differentiation and substitution that the given function is a solution. 2 y = y² +4₁ (ltl) < (7); 4 1 , y = 2tan 2t y = -y+t(t) > (0): ² y + 2 ,y = 3t+t y = 2y + 1(t) > (0); t t. -2(s² - t²) 2 ‚y = t_ Inty - 4ty = 1:,y = Se 0 ds
Verification For each differential equation, verify by differen. tiation and substitution that the given function is a solution. 1. yy² +4 (r</4): y = 2 tan 2 2. y = = y +1 (t> ( (1 0): y = 31 + 1² 2²/1 + 1 (1 > 0); 3. y 4. y 4ry = 1: y = r² Inr y = $₁² e-211²-1²) ds
Transcribed Image Text:Verification For each differential equation, verify by differen. tiation and substitution that the given function is a solution. 1. yy² +4 (r</4): y = 2 tan 2 2. y = = y +1 (t> ( (1 0): y = 31 + 1² 2²/1 + 1 (1 > 0); 3. y 4. y 4ry = 1: y = r² Inr y = $₁² e-211²-1²) ds
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