Screenshot at 20...->Assignments: Find a solution for the following equations in two different ways: analytically andnumerically, and compare the results estimating the errors. Do 3 steps only for thenumerical calculations for:Q1/1.Euler's method-y' = (y + x)², y(0) = 0, h = 0.1%3D2.Heun's Method-y' – xy² = 0, y(0) = 1, h = 0.13.Runge-Kutta (RK4)y' = 1 + y², y(0) = 0, h = 0.1%3D Screenshot at 20...->Assignments:y' + 5.2y = 19.4 sin 21, y(0) = 01.У — бу %3D 0, у(-1) %3D 42.y" – 6y' + 5y = 29 cos 2t, y(0) = 3.2,y'(0) = 6.23.y" + 3y' + 2y = 1 if 0 < t < 1 and 0 if t > 1;y(0) = 0, y'(0) = 04.5.y" + 2y' + 5y = 25t – 1008(ty'(0) = 5т), у(0) %3D — 2,

As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

ignments: Find a solution for the following equations in two different ways: analytically and numerically, and compare the results estimating the errors. Do 3 steps only for the numerical calculations for: 1/ 1. Euler's method -y' = (y + x)², y(0) = 0, h = 0.1 %3D

ignments: Find a solution for the following equations in two different ways: analytically and numerically, and compare the results estimating the errors. Do 3 steps only for the numerical calculations for: 1/ 1. Euler's method -y' = (y + x)², y(0) = 0, h = 0.1 %3D

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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Concept explainers

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

Screenshot at 20...
->
Assignments: Find a solution for the following equations in two different ways: analytically and
numerically, and compare the results estimating the errors. Do 3 steps only for the
numerical calculations for:
Q1/
1.
Euler's method
-y' = (y + x)², y(0) = 0, h = 0.1
%3D
2.
Heun's Method
-y' – xy² = 0, y(0) = 1, h = 0.1
3.
Runge-Kutta (RK4)
y' = 1 + y², y(0) = 0, h = 0.1
%3D

Screenshot at 20...
->
Assignments:
y' + 5.2y = 19.4 sin 21, y(0) = 0
1.
У — бу %3D 0, у(-1) %3D 4
2.
y" – 6y' + 5y = 29 cos 2t, y(0) = 3.2,
y'(0) = 6.2
3.
y" + 3y' + 2y = 1 if 0 < t < 1 and 0 if t > 1;
y(0) = 0, y'(0) = 0
4.
5.
y" + 2y' + 5y = 25t – 1008(t
y'(0) = 5
т), у(0) %3D — 2,

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