71.7.4 problem 4

Internal problem ID [14354]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.3.3, page 71
Problem number : 4
Date solved : Monday, March 31, 2025 at 12:19:03 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=\frac {y}{x -1}+x^{2} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.035 (sec). Leaf size: 23

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

\[ y = \left (\frac {x^{2}}{2}+x +\ln \left (x -1\right )-1-i \pi \right ) \left (x -1\right ) \]

✓ Mathematica. Time used: 0.06 (sec). Leaf size: 29

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

\[ y(x)\to (x-1) \left (\int _0^x\frac {K[1]^2}{K[1]-1}dK[1]-1\right ) \]

✓ Sympy. Time used: 0.278 (sec). Leaf size: 39

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

\[ y{\left (x \right )} = \frac {x^{3}}{2} + \frac {x^{2}}{2} + x \log {\left (x - 1 \right )} - x + x \left (-1 - i \pi \right ) - \log {\left (x - 1 \right )} + 1 + i \pi \]