71.9.6 problem 6

Internal problem ID [14485]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 4. N-th Order Linear Differential Equations. Exercises 4.1, page 186
Problem number : 6
Date solved : Tuesday, January 28, 2025 at 06:42:15 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} \left (x^{2}-4\right ) y^{\prime \prime }+y \ln \left (x \right )&=x \,{\mathrm e}^{x} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=1\\ y^{\prime }\left (1\right )&=2 \end{align*}

✗ Solution by Maple

dsolve([(x^2-4)*diff(y(x),x$2)+ln(x)*y(x)=x*exp(x),y(1) = 1, D(y)(1) = 2],y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[{(x^2-4)*D[y[x],{x,2}]+Log[x]*y[x]==x*Exp[x],{y[1]==1,Derivative[1][y][1]==2}},y[x],x,IncludeSingularSolutions -> True]
 

Not solved