83.12.2 problem 2

Internal problem ID [19174]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter III. Ordinary linear differential equations with constant coefficients. Exercise III (D) at page 37
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 01:10:54 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 24

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

\[ y(x)\to -5 x+c_1 e^x+c_2 e^{-x}-2 \]