please follow the format of the script given. thank you MATLAB can solve differential equations using the dsolve command.dsolve Symbolic solution of ordinary differential equations.Example:syms y(x)Dy (x) = diff(y)D2y(x) = diff(y, 2)yGS1 = dsolve (D2y+2*Dy+y==0)yGS2 = dsolve (D2y+2*Dy+y==0, y(0)==1, y(0)==2)Problems: Solve the following differential equations, using the initial conditions when applicable1. y₁" + 8y₁ + 16y₁ = 0, y₁ (0) = 1, y₁ (0) = 02. y₂" - 3y₂ + 2y₂ = 0, y₂(1) = 1, y₂ (1) = 43. Y3" + 8y₂ + 17y3 = 04. y + 8y + 16y4 = 05. y-729y5 = 0 1 %Solve the given Homogeneous Differential Equations with Constant Coefficients2 %Initialize the Variables345 %Solve the equation y"+8y'+16y=0, y(0)=1, y'(0)=0. Save your answer as y1¹;67 %Solve the equation y"-3y'+2y=0, y_2(1)=1, y_2¹ (1)=4. Save your answer as y2;89 %Solve the equation y"+8y'+17y=0. Save your answer as y3;1011 %Solve the equation y^{IV} + 8y" + 16y=0. Save your answer as 4;1213 %Solve the equation y^{VI}-729y=0. Save your answer as y1¹;141516

Answered: ve Symbolic solution of ordinary di…

Engineering

Computer Science

ve Symbolic solution of ordinary di ble: y (x) ) = diff(y)

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Concept explainers

LUP Decomposition

LU decomposition stands for Lower-Upper decomposition. LU decomposition is the factorization of the lower triangular matrix and an upper triangular matrix. It is very useful in linear algebra and numerical analysis. A permutation matrix is usually included in the product. Gaussian elimination in a matrix form is known as LU decomposition, When inverting a matrix or evaluating its determinant, this is a crucial step. Tadeusz Banachiewicz, a Polish mathematician, first proposed the LU decomposition in 1938.

Question

please follow the format of the script given. thank you

MATLAB can solve differential equations using the dsolve command.
dsolve Symbolic solution of ordinary differential equations.
Example:
syms y(x)
Dy (x) = diff(y)
D2y(x) = diff(y, 2)
yGS1 = dsolve (D2y+2*Dy+y==0)
yGS2 = dsolve (D2y+2*Dy+y==0, y(0)==1, y(0)==2)
Problems: Solve the following differential equations, using the initial conditions when applicable
1. y₁" + 8y₁ + 16y₁ = 0, y₁ (0) = 1, y₁ (0) = 0
2. y₂" - 3y₂ + 2y₂ = 0, y₂(1) = 1, y₂ (1) = 4
3. Y3" + 8y₂ + 17y3 = 0
4. y + 8y + 16y4 = 0
5. y-729y5 = 0

1 %Solve the given Homogeneous Differential Equations with Constant Coefficients
2 %Initialize the Variables
3
4
5 %Solve the equation y"+8y'+16y=0, y(0)=1, y'(0)=0. Save your answer as y1¹;
6
7 %Solve the equation y"-3y'+2y=0, y_2(1)=1, y_2¹ (1)=4. Save your answer as y2;
8
9 %Solve the equation y"+8y'+17y=0. Save your answer as y3;
10
11 %Solve the equation y^{IV} + 8y" + 16y=0. Save your answer as 4;
12
13 %Solve the equation y^{VI}-729y=0. Save your answer as y1¹;
14
15
16

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