41.2.30 problem 30

Internal problem ID [8732]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 1. First order differential equations. Section 1.2 Homogeneous equations problems. page 12
Problem number : 30
Date solved : Tuesday, September 30, 2025 at 05:45:57 PM
CAS classification : [_linear]

\begin{align*} x y^{\prime }&=x +\frac {y}{2} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.045 (sec). Leaf size: 13

ode:=x*diff(y(x),x) = x+1/2*y(x); 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 2 x +\sqrt {x}\, c_1 \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 17

ode=x*D[y[x],x]==x+1/2*y[x]; 
ic={y[0]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 2 x+c_1 \sqrt {x} \end{align*}

✗ Sympy

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

ValueError : Couldnt solve for initial conditions