44.2.10 problem 10

Internal problem ID [6942]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Section 1.2 Initial value problems. Exercises 1.2 at page 19
Problem number : 10
Date solved : Monday, January 27, 2025 at 02:37:41 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }+x&=0 \end{align*}

With initial conditions

\begin{align*} x \left (\frac {\pi }{4}\right )&=\sqrt {2}\\ x^{\prime }\left (\frac {\pi }{4}\right )&=2 \sqrt {2} \end{align*}

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 13

dsolve([diff(x(t),t$2)+x(t)=0,x(1/4*Pi) = 2^(1/2), D(x)(1/4*Pi) = 2*2^(1/2)],x(t), singsol=all)
 

\[ x \left (t \right ) = 3 \sin \left (t \right )-\cos \left (t \right ) \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 14

DSolve[{D[x[t],{t,2}]+x[t]==0,{x[Pi/4]==Sqrt[2],Derivative[1][x][Pi/4] == 2*Sqrt[2]}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to 3 \sin (t)-\cos (t) \]