15.6.4 problem 4

Internal problem ID [2961]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 10, page 41
Problem number : 4
Date solved : Sunday, March 30, 2025 at 01:02:11 AM
CAS classification : [[_linear, `class A`]]

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

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

ode:=diff(y(x),x) = y(x)+3*x^2*exp(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (x^{3}+c_1 \right ) {\mathrm e}^{x} \]

✓ Mathematica. Time used: 0.051 (sec). Leaf size: 15

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

\[ y(x)\to e^x \left (x^3+c_1\right ) \]

✓ Sympy. Time used: 0.135 (sec). Leaf size: 10

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

\[ y{\left (x \right )} = \left (C_{1} + x^{3}\right ) e^{x} \]