15.14.25 problem 25

Internal problem ID [3197]
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 : 25
Date solved : Monday, January 27, 2025 at 07:25:52 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=x^{2} {\mathrm e}^{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 33

dsolve(diff(y(x),x$3)-6*diff(y(x),x$2)+11*diff(y(x),x)-6*y(x)=x^2*exp(2*x),y(x), singsol=all)
 

\[ y = \frac {\left (-x^{3}+3 c_2 -6 x \right ) {\mathrm e}^{2 x}}{3}+{\mathrm e}^{x} c_{1} +c_3 \,{\mathrm e}^{3 x} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 37

DSolve[D[y[x],{x,3}]-6*D[y[x],{x,2}]+11*D[y[x],x]-6*y[x]==x^2*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x \left (e^x \left (-\frac {x^3}{3}-2 x+c_2\right )+c_3 e^{2 x}+c_1\right ) \]