Internal problem ID [2260]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {x^{2} y^{\prime \prime }-y^{\prime } x +2 y=x^{2} \ln \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y = \sin \left (\ln \left (x \right )\right ) x c_{2} +\cos \left (\ln \left (x \right )\right ) x c_{1} +\frac {x^{2} \left (\ln \left (x \right )-1\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.078 (sec). Leaf size: 31
DSolve[x^2*y''[x]-x*y'[x]+2*y[x]==x^2*Log[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} x (x (\log (x)-1)+2 c_2 \cos (\log (x))+2 c_1 \sin (\log (x))) \]