find a second solution y2x using reduction of order 1 x2y xy 2y 0 y1 x sinln x answer y2 x cosln

Name: find a second solution y2x using reduction of order 1 x2y xy 2y 0 y1 x sinln x answer y2 x cosln x 2 1 2x x2y 21 xy 2y 0 y1 x 1 answer y2 x2 x 2 98786
Uploaded: 2023-05-31T16:55:39-08:00
Duration: 2 min 20 s
Channel: Madhur L
Description: find a second solution y2x using reduction of order 1 x2y xy 2y 0 y1 x sinln x answer y2 x cosln x 2 1 2x x2y 21 xy 2y 0 y1 x 1 answer y2 x2 x 2 98786

Question

Tim Thornhill · Accepted Answer

1. For the first equation, we first find the complementary solution by assuming y = e^(rx). Subs

Question

Find a second solution y2(x), using reduction of order: 1. x^2y'' − xy' + 2y = 0; y1 = x sin(ln x) Answer: y2 = x cos(ln x) 2. (1 − 2x − x^2)y'' + 2(1 + x)y' − 2y = 0; y1 = x + 1 Answer: y2 = x^2 + x + 2

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