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LineaY solve this System (x(0), y(0)) = (3,-4) %3D %3D Find the Particalay soloution

LineaY solve this System (x(0), y(0)) = (3,-4) %3D %3D Find the Particalay soloution

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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Solve the system and give me particular solution of this. And solve exactly by the same method number 2 that i attached and highlith. So solve exactly the s same method to solve this question and also draw a graph And take a thumb up
Lineay solve this System {x'=y (x(0), y(0)) = (3,-4) %3D %3D Fint the Particalay Baloution.
Transcribed Image Text:Lineay solve this System {x'=y (x(0), y(0)) = (3,-4) %3D %3D Fint the Particalay Baloution.
23 Phase Plane Analysis Example 108. Solve the following system with (ro. o) = (1,0). unew genen!, = -toy ot to. Method 1. Solve r equation first, then the y equation. We can do this because the equation is independent of y: Solve the x equation first: Ex. exp In a= -t+e I= Ae z(0) = A = 1 Then solve the y equation: y'= x 2nd dy dy: y = -e + C (X, yo) = U,0) 0 = -| +c - C=| particubor 2 yC6) = -e t1 Method 2: Divide the second equation by the first. -X y'--x' relationship y = -z+ bstween sole 0= -1+c=c=1 y =1-1 (x. Y) Now plot x-y coordinates where t is implicit. Which way do trajectories travel? Since (z(0), y(0)) = (1,0), that's where they start. Or we have: Pquilibria ? x( Net y= X table メニo → X=0 Vector dec *く。 forr lalt inc any Y *(4) (a) y>0 indicates that y is increasing (b) <0 indicates that x is decreasing s tam
Transcribed Image Text:23 Phase Plane Analysis Example 108. Solve the following system with (ro. o) = (1,0). unew genen!, = -toy ot to. Method 1. Solve r equation first, then the y equation. We can do this because the equation is independent of y: Solve the x equation first: Ex. exp In a= -t+e I= Ae z(0) = A = 1 Then solve the y equation: y'= x 2nd dy dy: y = -e + C (X, yo) = U,0) 0 = -| +c - C=| particubor 2 yC6) = -e t1 Method 2: Divide the second equation by the first. -X y'--x' relationship y = -z+ bstween sole 0= -1+c=c=1 y =1-1 (x. Y) Now plot x-y coordinates where t is implicit. Which way do trajectories travel? Since (z(0), y(0)) = (1,0), that's where they start. Or we have: Pquilibria ? x( Net y= X table メニo → X=0 Vector dec *く。 forr lalt inc any Y *(4) (a) y>0 indicates that y is increasing (b) <0 indicates that x is decreasing s tam
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