38.3.7 problem 7

Internal problem ID [6485]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 25. Second order differential equations. Test Excercise 25. page 1093
Problem number : 7
Date solved : Monday, January 27, 2025 at 02:07:38 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 3 y^{\prime \prime }-2 y^{\prime }-y&=2 x -3 \end{align*}

✓ Solution by Maple

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

dsolve(3*diff(y(x),x$2)-2*diff(y(x),x)-y(x)=2*x-3,y(x), singsol=all)
 

\[ y = {\mathrm e}^{-\frac {x}{3}} c_2 +{\mathrm e}^{x} c_1 -2 x +7 \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 26

DSolve[3*D[y[x],{x,2}]-2*D[y[x],x]-y[x]==2*x-3,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -2 x+c_1 e^{-x/3}+c_2 e^x+7 \]