84.18.6 problem 10.14

Internal problem ID [22203]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 10. Linear differential equations. General remarks. Supplementary problems
Problem number : 10.14
Date solved : Thursday, October 02, 2025 at 08:34:04 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.000 (sec). Leaf size: 13

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

\[ y = c_1 \,{\mathrm e}^{\frac {x \left (x +4\right )}{2}} \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 23

ode=D[y[x],{x,1}]-2*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+4)}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.227 (sec). Leaf size: 12

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

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