15.12.7 problem 7

Internal problem ID [3151]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 20, page 90
Problem number : 7
Date solved : Tuesday, March 04, 2025 at 04:03:36 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-y&=3 x +5 \,{\mathrm e}^{x} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 26

ode:=diff(diff(y(x),x),x)-y(x) = 3*x+5*exp(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-x} c_{1} +\frac {\left (10 x +4 c_2 -5\right ) {\mathrm e}^{x}}{4}-3 x \]

✓ Mathematica. Time used: 0.212 (sec). Leaf size: 32

ode=D[y[x],{x,2}]-y[x]==3*x+5*Exp[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -3 x+e^x \left (\frac {5 x}{2}-\frac {5}{4}+c_1\right )+c_2 e^{-x} \]

✓ Sympy. Time used: 0.093 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*x - y(x) - 5*exp(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{2} e^{- x} - 3 x + \left (C_{1} + \frac {5 x}{2}\right ) e^{x} \]