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Find the general solution for the following ODE. State which rule you are using. If the initial condition is given find the particular solution. 6e2x 1) (D² - 4D+41)y= = 3r

Find the general solution for the following ODE. State which rule you are using. If the initial condition is given find the particular solution. 6e2x 1) (D² - 4D+41)y= = 3r

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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Find the general solution for the following ODE. State which rule you are using. If the initial condition is given find the particular solution. 1) (D² - 4D+41)y=- 6e²x x4 2) (D² +6D+91)y= 16e-3x x² +1 3) (x²D² - 2xD +21) y = x³ sin x = 4) (x²D² + xD-I)y=16x³ 5) (x³D³ + xD-1)y=x² ; 6) (4x³D³ +3xD-31)y=10 ; y(1)=-1 y(1) = 1 ; ; y'(1) = 1 y'(1) = 3 ; y"(1) = 14
Transcribed Image Text:Find the general solution for the following ODE. State which rule you are using. If the initial condition is given find the particular solution. 1) (D² - 4D+41)y=- 6e²x x4 2) (D² +6D+91)y= 16e-3x x² +1 3) (x²D² - 2xD +21) y = x³ sin x = 4) (x²D² + xD-I)y=16x³ 5) (x³D³ + xD-1)y=x² ; 6) (4x³D³ +3xD-31)y=10 ; y(1)=-1 y(1) = 1 ; ; y'(1) = 1 y'(1) = 3 ; y"(1) = 14
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