71.1.162 problem 189 (page 297)

Internal problem ID [19338]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 189 (page 297)
Date solved : Sunday, October 12, 2025 at 05:34:12 AM
CAS classification : system_of_ODEs

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

✓ Maple. Time used: 0.089 (sec). Leaf size: 36

ode:=[diff(y(x),x)+2*z(x)/x^2 = 1, diff(z(x),x)+y(x) = x]; 
dsolve(ode);
 

\begin{align*} y \left (x \right ) &= \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*}

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

ode={D[y[x],x]+2*z[x]/x^2==1,D[z[x],x]+y[x]==x}; 
ic={}; 
DSolve[{ode,ic},{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*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
z = Function("z") 
ode=[Eq(Derivative(y(x), x) - 1 + 2*z(x)/x**2,0),Eq(-x + y(x) + Derivative(z(x), x),0)] 
ics = {} 
dsolve(ode,func=[y(x),z(x)],ics=ics)
 

NotImplementedError :