15.16.11 problem 11

Internal problem ID [3231]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 25, page 112
Problem number : 11
Date solved : Monday, January 27, 2025 at 07:26:56 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 26

dsolve(x^2*diff(y(x),x$2)-x*diff(y(x),x)+2*y(x)=x^2*ln(x),y(x), singsol=all)
 

\[ y = \frac {x \left (2 \cos \left (\ln \left (x \right )\right ) c_{1} +2 \sin \left (\ln \left (x \right )\right ) c_2 +x \left (-1+\ln \left (x \right )\right )\right )}{2} \]

✓ Solution by Mathematica

Time used: 0.084 (sec). Leaf size: 31

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

\[ y(x)\to \frac {1}{2} x (x (\log (x)-1)+2 c_2 \cos (\log (x))+2 c_1 \sin (\log (x))) \]