15.11.12 problem 12

Internal problem ID [3122]
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 : 12
Date solved : Monday, January 27, 2025 at 07:21:08 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 29

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

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

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 54

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

\[ y(x)\to e^x \left (x+c_2 e^{x/2} \cos \left (\frac {\sqrt {3} x}{2}\right )+c_1 e^{x/2} \sin \left (\frac {\sqrt {3} x}{2}\right )+1\right ) \]