83.15.2 problem 2

Internal problem ID [19187]
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 (G) at page 45
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 01:11:51 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 21

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

\[ y \left (x \right ) = c_{2} {\mathrm e}^{-x}+\left (c_3 x +c_{1} \right ) {\mathrm e}^{x}+x +1 \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 29

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

\[ y(x)\to x+c_3 e^x x+c_1 e^{-x}+c_2 e^x+1 \]