64.5.36 problem 40

Internal problem ID [13278]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.3 (Linear equations). Exercises page 56
Problem number : 40
Date solved : Monday, March 31, 2025 at 07:45:00 AM
CAS classification : [_Riccati]

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

✓ Maple. Time used: 0.017 (sec). Leaf size: 53

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

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

✓ Mathematica. Time used: 0.147 (sec). Leaf size: 45

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

\begin{align*} y(x)\to x+\frac {e^{-\frac {x^2}{2}}}{\sqrt {\frac {\pi }{2}} \text {erf}\left (\frac {x}{\sqrt {2}}\right )+c_1} \\ y(x)\to x \\ \end{align*}

✗ Sympy

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

TypeError : bad operand type for unary -: list