85.35.2 problem 2

Internal problem ID [22722]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. C Exercises at page 68
Problem number : 2
Date solved : Thursday, October 02, 2025 at 09:13:51 PM
CAS classification : [_linear]

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

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

ode:=diff(y(x),x)+x*y(x) = x^2+1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x +{\mathrm e}^{-\frac {x^{2}}{2}} c_1 \]

✓ Mathematica. Time used: 0.053 (sec). Leaf size: 19

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

\begin{align*} y(x)&\to x+c_1 e^{-\frac {x^2}{2}} \end{align*}

✓ Sympy. Time used: 0.130 (sec). Leaf size: 12

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

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