35.2.10 problem 10

Internal problem ID [6102]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 2. Separable equations. page 398
Problem number : 10
Date solved : Sunday, March 30, 2025 at 10:38:50 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Maple. Time used: 0.022 (sec). Leaf size: 14

ode:=diff(y(x),x)-x*y(x) = x; 
ic:=y(0) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.071 (sec). Leaf size: 20

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

\[ y(x)\to 2 e^{\frac {1}{2} \left (x^2-1\right )}-1 \]

✓ Sympy. Time used: 0.292 (sec). Leaf size: 12

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

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