40.4.2 problem 19 (c)

Internal problem ID [6642]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 6. Equations of first order and first degree (Linear equations). Supplemetary problems. Page 39
Problem number : 19 (c)
Date solved : Sunday, March 30, 2025 at 11:13:11 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 13

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

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

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 23

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

\begin{align*} y(x)\to c_1 e^{\frac {1}{2} x (x+2)} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.282 (sec). Leaf size: 12

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)
 

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