87.4.23 problem 34

Internal problem ID [23289]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 1. Elementary methods. First order differential equations. Exercise at page 37
Problem number : 34
Date solved : Thursday, October 02, 2025 at 09:28:44 PM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (5\right )&=24 \\ \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 9

ode:=(1-x)*diff(y(x),x)+x*y(x) = x*(x-1)^2; 
ic:=[y(5) = 24]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = x^{2}-1 \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 10

ode=(1-x)*D[y[x],x]+x*y[x]==x*(x-1)^2; 
ic={y[5]==24}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x^2-1 \end{align*}

✓ Sympy. Time used: 0.201 (sec). Leaf size: 7

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*(x - 1)**2 + x*y(x) + (1 - x)*Derivative(y(x), x),0) 
ics = {y(5): 24} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x^{2} - 1 \]