78.2.16 problem 5.f

Internal problem ID [20968]
Book : A FIRST COURSE IN DIFFERENTIAL EQUATIONS FOR SCIENTISTS AND ENGINEERS. By Russell Herman. University of North Carolina Wilmington. LibreText. compiled on 06/09/2025
Section : Chapter 2, Second order ODEs. Problems section 2.6
Problem number : 5.f
Date solved : Thursday, October 02, 2025 at 07:00:48 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 24

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

\[ y = -{\mathrm e}^{-x} c_1 -3 x^{2}+x^{3}+6 x +c_2 \]

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 28

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

\begin{align*} y(x)&\to x^3-3 x^2+6 x-c_1 e^{-x}+c_2 \end{align*}

✓ Sympy. Time used: 0.079 (sec). Leaf size: 20

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

\[ y{\left (x \right )} = C_{1} + C_{2} e^{- x} + x^{3} - 3 x^{2} + 6 x \]