84.13.5 problem 7.6

Internal problem ID [22155]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 7. Integrating factors. Solved problems. Page 29
Problem number : 7.6
Date solved : Thursday, October 02, 2025 at 08:32:54 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 12

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

\[ y = \frac {1}{2}+{\mathrm e}^{x^{2}} c_1 \]

✓ Mathematica. Time used: 0.032 (sec). Leaf size: 24

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

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

✓ Sympy. Time used: 0.174 (sec). Leaf size: 12

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

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