77.1.152 problem 179 (page 297)

Internal problem ID [18042]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 179 (page 297)
Date solved : Tuesday, January 28, 2025 at 11:23:22 AM
CAS classification : system_of_ODEs

\begin{align*} y^{\prime }&=-z \left (x \right )\\ z^{\prime }\left (x \right )&=y \end{align*}

With initial conditions

\begin{align*} y \left (0\right ) = 1\\ z \left (0\right ) = 0 \end{align*}

✓ Solution by Maple

Time used: 0.052 (sec). Leaf size: 11

dsolve([diff(y(x),x) = -z(x), diff(z(x),x) = y(x), y(0) = 1, z(0) = 0], singsol=all)
 

\begin{align*} y &= \cos \left (x \right ) \\ z \left (x \right ) &= \sin \left (x \right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 12

DSolve[{D[y[x],x]==-z[x],D[z[x],x]==y[x]},{y[0]==1,z[0]==0},{y[x],z[x]},x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \cos (x) \\ z(x)\to \sin (x) \\ \end{align*}