15.14.20 problem 20

Internal problem ID [3192]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 23, page 106
Problem number : 20
Date solved : Monday, January 27, 2025 at 07:25:49 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }-5 y^{\prime }&=x^{2} {\mathrm e}^{-x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 41

dsolve(diff(y(x),x$3)+4*diff(y(x),x$2)-5*diff(y(x),x)=x^2*exp(-x),y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{-5 x} \left (\left (x^{2}+\frac {5}{2} x +\frac {23}{8}\right ) {\mathrm e}^{4 x}+8 c_{1} {\mathrm e}^{6 x}+8 c_3 \,{\mathrm e}^{5 x}-\frac {8 c_2}{5}\right )}{8} \]

✓ Solution by Mathematica

Time used: 0.289 (sec). Leaf size: 44

DSolve[D[y[x],{x,3}]+4*D[y[x],{x,2}]-5*D[y[x],x]==x^2*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{64} e^{-x} \left (8 x^2+20 x+23\right )-\frac {1}{5} c_1 e^{-5 x}+c_2 e^x+c_3 \]