83.16.1 problem 1

Internal problem ID [19190]
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 (H) at page 47
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 01:11:53 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 30

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

\[ y \left (x \right ) = \frac {{\mathrm e}^{-2 x} \left (\left (6 c_3 x +x^{2}+6 c_{1} \right ) {\mathrm e}^{3 x}+6 c_{2} \right )}{6} \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 39

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

\[ y(x)\to e^x \left (\frac {x^2}{6}+\left (-\frac {1}{9}+c_3\right ) x+\frac {1}{27}+c_2\right )+c_1 e^{-2 x} \]