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 : Monday, January 27, 2025 at 03:08:47 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

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

dsolve(6*diff(y(x),x$2)+5*diff(y(x),x)-6*y(x)=x,y(x), singsol=all)
 

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

✓ Solution by Mathematica

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

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

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