83.11.12 problem 12

Internal problem ID [22001]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Chapter VI. Linear equations with constant coefficients. Ex. XIII at page 106
Problem number : 12
Date solved : Thursday, October 02, 2025 at 08:21:34 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }-y^{\prime }&=6 x^{5} {\mathrm e}^{x} \end{align*}

✓ Maple. Time used: 0.000 (sec). Leaf size: 38

ode:=diff(diff(y(x),x),x)-diff(y(x),x) = 6*x^5*exp(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (x^{6}-6 x^{5}+30 x^{4}-120 x^{3}+360 x^{2}+c_1 -720 x +720\right ) {\mathrm e}^{x}+c_2 \]

✓ Mathematica. Time used: 0.041 (sec). Leaf size: 42

ode=D[y[x],{x,2}]-D[y[x],x]==6*x^5*Exp[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^x \left (x^6-6 x^5+30 x^4-120 x^3+360 x^2-720 x+720+c_1\right )+c_2 \end{align*}

✓ Sympy. Time used: 0.157 (sec). Leaf size: 36

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-6*x**5*exp(x) - Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + \left (C_{2} + x^{6} - 6 x^{5} + 30 x^{4} - 120 x^{3} + 360 x^{2} - 720 x\right ) e^{x} \]