84.16.4 problem 8.13

Internal problem ID [22184]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 8. Linear first-order differential equations. Supplementary problems
Problem number : 8.13
Date solved : Thursday, October 02, 2025 at 08:33:41 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

ode:=diff(y(x),x)+x^2*y(x) = x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = 1+{\mathrm e}^{-\frac {x^{3}}{3}} c_1 \]

✓ Mathematica. Time used: 0.035 (sec). Leaf size: 24

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

\begin{align*} y(x)&\to 1+c_1 e^{-\frac {x^3}{3}}\\ y(x)&\to 1 \end{align*}

✓ Sympy. Time used: 0.190 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = C_{1} e^{- \frac {x^{3}}{3}} + 1 \]