77.1.162 problem 189 (page 297)

Internal problem ID [18052]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 189 (page 297)
Date solved : Tuesday, January 28, 2025 at 08:28:31 PM
CAS classification : system_of_ODEs

\begin{align*} y^{\prime }+\frac {2 z \left (x \right )}{x^{2}}&=1\\ z^{\prime }\left (x \right )+y&=x \end{align*}

✓ Solution by Maple

Time used: 0.075 (sec). Leaf size: 36

dsolve([diff(y(x),x)+2*z(x)/x^2=1,diff(z(x),x)+y(x)=x],singsol=all)
 

\begin{align*} y &= \frac {c_{2} x^{3}+c_{1}}{x^{2}} \\ z \left (x \right ) &= \frac {-c_{2} x^{3}+x^{3}+2 c_{1}}{2 x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 43

DSolve[{D[y[x],x]+2*z[x]/x^2==1,D[z[x],x]+y[x]==x},{y[x],z[x]},x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {c_1}{x^2}+\left (\frac {1}{3}+c_2\right ) x \\ z(x)\to \frac {1}{6} (2-3 c_2) x^2+\frac {c_1}{x} \\ \end{align*}