87.16.22 problem 22

Internal problem ID [23591]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 119
Problem number : 22
Date solved : Thursday, October 02, 2025 at 09:43:17 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 25

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

\[ y = \sin \left (\sqrt {2}\, x \right ) c_2 +\cos \left (\sqrt {2}\, x \right ) c_1 +\frac {{\mathrm e}^{x}}{3} \]

✓ Mathematica. Time used: 0.075 (sec). Leaf size: 35

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

\begin{align*} y(x)&\to \frac {e^x}{3}+c_1 \cos \left (\sqrt {2} x\right )+c_2 \sin \left (\sqrt {2} x\right ) \end{align*}

✓ Sympy. Time used: 0.060 (sec). Leaf size: 27

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

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