69.1.104 problem 151

Internal problem ID [14257]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 151
Date solved : Tuesday, January 28, 2025 at 06:23:26 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

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

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

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