15.11.11 problem 11

Internal problem ID [3121]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 19, page 86
Problem number : 11
Date solved : Monday, January 27, 2025 at 07:21:05 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=x^{3} \end{align*}

✓ Solution by Maple

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

dsolve(diff(y(x),x$2)-diff(y(x),x)-6*y(x)=x^3,y(x), singsol=all)
 

\[ y = -\frac {{\mathrm e}^{-2 x} \left (\left (x^{3}-\frac {1}{2} x^{2}+\frac {7}{6} x -\frac {13}{36}\right ) {\mathrm e}^{2 x}-6 \,{\mathrm e}^{5 x} c_2 -6 c_{1} \right )}{6} \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 41

DSolve[D[y[x],{x,2}]-D[y[x],x]-6*y[x]==x^3,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{216} \left (-36 x^3+18 x^2-42 x+13\right )+c_1 e^{-2 x}+c_2 e^{3 x} \]