56.25.1 problem Ex 1

Internal problem ID [14214]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter VII, Linear differential equations with constant coefficients. Article 48. Page 103
Problem number : Ex 1
Date solved : Thursday, October 02, 2025 at 09:26:46 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

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

\[ y = \left (-x +{\mathrm e}^{x} c_1 +c_2 \right ) {\mathrm e}^{x} \]

✓ Mathematica. Time used: 0.046 (sec). Leaf size: 22

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

\begin{align*} y(x)&\to e^x \left (-x+c_2 e^x-1+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.107 (sec). Leaf size: 14

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

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