34.7.3 problem 12

Internal problem ID [7980]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 12. Linear equations of order n. Supplemetary problems. Page 81
Problem number : 12
Date solved : Tuesday, September 30, 2025 at 05:13:49 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{5 x} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 19

ode:=diff(diff(y(x),x),x)-3*diff(y(x),x)+2*y(x) = exp(5*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (\frac {{\mathrm e}^{4 x}}{12}+{\mathrm e}^{x} c_1 +c_2 \right ) {\mathrm e}^{x} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 29

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

\begin{align*} y(x)&\to \frac {e^{5 x}}{12}+c_1 e^x+c_2 e^{2 x} \end{align*}

✓ Sympy. Time used: 0.114 (sec). Leaf size: 19

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

\[ y{\left (x \right )} = \left (C_{1} + C_{2} e^{x} + \frac {e^{4 x}}{12}\right ) e^{x} \]