87.2.10 problem 10

Internal problem ID [23245]
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 17
Problem number : 10
Date solved : Thursday, October 02, 2025 at 09:26:45 PM
CAS classification : [_linear]

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

With initial conditions

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 5

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

\[ y = x \]

✓ Mathematica. Time used: 0.104 (sec). Leaf size: 6

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

\begin{align*} y(x)&\to x \end{align*}

✓ Sympy. Time used: 0.129 (sec). Leaf size: 3

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

\[ y{\left (x \right )} = x \]