40.4.19 problem 22 (a)

Internal problem ID [6659]
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 : 22 (a)
Date solved : Sunday, March 30, 2025 at 11:15:15 AM
CAS classification : [_linear]

\begin{align*} x y^{\prime }&=2 y+x^{3} {\mathrm e}^{x} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.033 (sec). Leaf size: 15

ode:=x*diff(y(x),x) = 2*y(x)+x^3*exp(x); 
ic:=y(1) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.056 (sec). Leaf size: 16

ode=x*D[y[x],x]==2*y[x]+x^3*Exp[x]; 
ic={y[1]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \left (e^x-e\right ) x^2 \]

✓ Sympy. Time used: 0.301 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**3*exp(x) + x*Derivative(y(x), x) - 2*y(x),0) 
ics = {y(1): 0} 
dsolve(ode,func=y(x),ics=ics)
 

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