23.3.91 problem 93

Internal problem ID [5805]
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 : 93
Date solved : Tuesday, September 30, 2025 at 02:03:33 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 12 y-7 y^{\prime }+y^{\prime \prime }&=x \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

ode:=12*y(x)-7*diff(y(x),x)+diff(diff(y(x),x),x) = x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{4 x} c_2 +{\mathrm e}^{3 x} c_1 +\frac {x}{12}+\frac {7}{144} \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 30

ode=12*y[x] - 7*D[y[x],x] + D[y[x],{x,2}] == x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x}{12}+c_1 e^{3 x}+c_2 e^{4 x}+\frac {7}{144} \end{align*}

✓ Sympy. Time used: 0.110 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x + 12*y(x) - 7*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{3 x} + C_{2} e^{4 x} + \frac {x}{12} + \frac {7}{144} \]