49.6.10 problem 1(j)

Internal problem ID [7638]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 2. Linear equations with constant coefficients. Page 69
Problem number : 1(j)
Date solved : Wednesday, March 05, 2025 at 04:49:26 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 29

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

\[ y = -\frac {{\mathrm e}^{-\frac {3 x}{2}} \left (\left (x +\frac {5}{6}\right ) {\mathrm e}^{\frac {3 x}{2}}-6 \,{\mathrm e}^{\frac {13 x}{6}} c_{1} -6 c_{2} \right )}{6} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 34

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

\[ y(x)\to -\frac {x}{6}+c_1 e^{2 x/3}+c_2 e^{-3 x/2}-\frac {5}{36} \]

✓ Sympy. Time used: 0.230 (sec). Leaf size: 26

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

\[ y{\left (x \right )} = C_{1} e^{- \frac {3 x}{2}} + C_{2} e^{\frac {2 x}{3}} - \frac {x}{6} - \frac {5}{36} \]