23.3.87 problem 89

Internal problem ID [5801]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 3. THE DIFFERENTIAL EQUATION IS LINEAR AND OF SECOND ORDER, page 311
Problem number : 89
Date solved : Tuesday, September 30, 2025 at 02:03:31 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 32

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

\[ y = {\mathrm e}^{3 x} c_2 +{\mathrm e}^{2 x} c_1 +\frac {{\mathrm e}^{a x}}{a^{2}-5 a +6} \]

✓ Mathematica. Time used: 0.039 (sec). Leaf size: 54

ode=6*y[x] - 5*D[y[x],x] + D[y[x],{x,2}] == E^(a*x); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {e^{2 x} \left (\left (a^2-5 a+6\right ) c_2 e^x+\left (a^2-5 a+6\right ) c_1+e^{(a-2) x}\right )}{(a-3) (a-2)} \end{align*}

✓ Sympy. Time used: 0.133 (sec). Leaf size: 29

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

\[ y{\left (x \right )} = C_{1} e^{2 x} + C_{2} e^{3 x} + \frac {e^{a x}}{a^{2} - 5 a + 6} \]