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dy 1 dx √1-x² ; y(0) = 0 dy=x√√x² +9; y(-4) = 0 dx dy dx = = re-* ; y(0) =1

dy 1 dx √1-x² ; y(0) = 0 dy=x√√x² +9; y(-4) = 0 dx dy dx = = re-* ; y(0) =1

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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1. Find a function y = f(x) satisfying the given differential equation and the prescribed initial condition. a. dy dx C. 1 √1-x² dy b. =x√x² +9; y(-4)= 0 dx dy dx ; y(0) = 0 = re-* ; y(0) =1 2. Express the solution of the initial value problem 2x = y + 2x cos(x); y(1) = 0 dy dx tv as an integral. 3. Find general solutions (implicit if necessary, explicit if convenient) of the given differ- ential equations. Primes denote derivatives with respect to x. a. y' = 1 + x + y + xy b. (1-²) dy dx C = 2y 2 A G
Transcribed Image Text:1. Find a function y = f(x) satisfying the given differential equation and the prescribed initial condition. a. dy dx C. 1 √1-x² dy b. =x√x² +9; y(-4)= 0 dx dy dx ; y(0) = 0 = re-* ; y(0) =1 2. Express the solution of the initial value problem 2x = y + 2x cos(x); y(1) = 0 dy dx tv as an integral. 3. Find general solutions (implicit if necessary, explicit if convenient) of the given differ- ential equations. Primes denote derivatives with respect to x. a. y' = 1 + x + y + xy b. (1-²) dy dx C = 2y 2 A G
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