4) Solve the system of differential equations dx =-2y+t dt dy using differential operators of the form Dy=- dt dy =-3x + 2t -1 dt Note for example that (D+5)(3t+ 2)= 3+15t+10 =15t +13 Solve for x(t) first, then solve for y(t). There should only be two parameters, and C2 in x(t) and y(t).

4) Solve the system of differential equations dx =-2y+t dt dy using differential operators of the form Dy=- dt dy =-3x + 2t -1 dt Note for example that (D+5)(3t+ 2)= 3+15t+10 =15t +13 Solve for x(t) first, then solve for y(t). There should only be two parameters, and C2 in x(t) and y(t).

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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

4)
Solve the system of differential equations
dx
=-2y +t
dt
using differential operators of the form Dy=
dt
dy
-3x +2t-1
dt
Note for example that (D+5)(3t+2)=3+15t+10 =15t +13
Solve for x(t) first, then solve for y(t). There should only be two parameters, c, and c,
in x(t) and y(t).

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