85.33.81 problem 82

Internal problem ID [22704]
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. A Exercises at page 65
Problem number : 82
Date solved : Thursday, October 02, 2025 at 09:11:13 PM
CAS classification : [_Bernoulli]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 35

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

\[ y = \frac {2 \,{\mathrm e}^{\frac {x^{2}}{2}}}{i \sqrt {\pi }\, \sqrt {2}\, \operatorname {erf}\left (\frac {i \sqrt {2}\, x}{2}\right )+2 c_1} \]

✗ Mathematica

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

Not solved

✓ Sympy. Time used: 0.197 (sec). Leaf size: 32

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

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