Internal problem ID [2254]
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: 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {2 x^{2} y^{\prime \prime }-3 y^{\prime } x -18 y=\ln \left (x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
dsolve(2*x^2*diff(y(x),x$2)-3*x*diff(y(x),x)-18*y(x)=ln(x),y(x), singsol=all)
\[ y = x^{\frac {9}{2}} c_{2} +\frac {c_{1}}{x^{2}}-\frac {\ln \left (x \right )}{18}+\frac {5}{324} \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 29
DSolve[2*x^2*y''[x]-3*x*y'[x]-18*y[x]==Log[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 x^{9/2}+\frac {c_1}{x^2}-\frac {\log (x)}{18}+\frac {5}{324} \]