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c) d'y 1 dy + dx² x dx = 0, x > 0, y₁ = ln x

c) d'y 1 dy + dx² x dx = 0, x > 0, y₁ = ln x

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
Question 1C
1. Show that given function is a solution of the differential equation. Then solve the equation by finding a general solution. b) c) d) d'y 1 dy dx² x dx x² d'y dx d'y dx² + 2x 1 dy x dx e) (1-x²). - 4x²y = 0, -∞ < x < ₁ = ² d'y dx² dy ·+ (x² + 2)y = 0, x > 0, y₁ = x sin x dx -= 0, x > 0, y₁ = ln x d²y_1 dy + 4x²y = 0, x > 0, y₁ = sin(x²) dx² x dx 2x. dy + 2y = 0, -1 < x < 1, y₁ = x dx 30
Transcribed Image Text:1. Show that given function is a solution of the differential equation. Then solve the equation by finding a general solution. b) c) d) d'y 1 dy dx² x dx x² d'y dx d'y dx² + 2x 1 dy x dx e) (1-x²). - 4x²y = 0, -∞ < x < ₁ = ² d'y dx² dy ·+ (x² + 2)y = 0, x > 0, y₁ = x sin x dx -= 0, x > 0, y₁ = ln x d²y_1 dy + 4x²y = 0, x > 0, y₁ = sin(x²) dx² x dx 2x. dy + 2y = 0, -1 < x < 1, y₁ = x dx 30
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