84.5.8 problem 3.2 (d)

Internal problem ID [22095]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 3. Classification of first-order differential equations. Solved problems. Page 11
Problem number : 3.2 (d)
Date solved : Thursday, October 02, 2025 at 08:24:42 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=\frac {y+x^{2}}{x^{3}} \end{align*}

✓ Maple. Time used: 0.000 (sec). Leaf size: 22

ode:=diff(y(x),x) = (y(x)+x^2)/x^3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (\frac {\operatorname {Ei}_{1}\left (-\frac {1}{2 x^{2}}\right )}{2}+c_1 \right ) {\mathrm e}^{-\frac {1}{2 x^{2}}} \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 33

ode=D[y[x],x]==(x^2+y[x])/( x^3 ); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{2} e^{-\frac {1}{2 x^2}} \left (-\operatorname {ExpIntegralEi}\left (\frac {1}{2 x^2}\right )+2 c_1\right ) \end{align*}

✓ Sympy. Time used: 2.003 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (x**2 + y(x))/x**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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