84.11.3 problem 6.3

Internal problem ID [22140]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 6. Exact first-order differential equations. Solved problems. Page 24
Problem number : 6.3
Date solved : Thursday, October 02, 2025 at 08:31:40 PM
CAS classification : [_linear]

\begin{align*} y x +x^{2}-y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 34

ode:=x*y(x)+x^2-diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.046 (sec). Leaf size: 48

ode=(x*y[x]+x^2)-D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.323 (sec). Leaf size: 41

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

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