83.44.4 problem Ex 4 page 36

Internal problem ID [19532]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter III. Ordinary linear differential equations with constant coefficients
Problem number : Ex 4 page 36
Date solved : Tuesday, January 28, 2025 at 01:49:56 PM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 22

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

\[ y \left (x \right ) = -\frac {{\mathrm e}^{-x}}{4}+\left (\left (x -1\right ) c_{1} +c_{2} \right ) {\mathrm e}^{x}+c_3 \]

✓ Solution by Mathematica

Time used: 0.077 (sec). Leaf size: 30

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

\[ y(x)\to -\frac {e^{-x}}{4}+e^x (c_2 (x-1)+c_1)+c_3 \]