Internal problem ID [2255]
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: 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {2 x^{2} y^{\prime \prime }-3 y^{\prime } x +2 y=\ln \left (x^{2}\right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(2*x^2*diff(y(x),x$2)-3*x*diff(y(x),x)+2*y(x)=ln(x^2),y(x), singsol=all)
\[ y \left (x \right ) = \frac {5}{2}+\frac {\ln \left (x^{2}\right )}{2}+\frac {2 c_{1} x^{2}}{3}+\sqrt {x}\, c_{2} \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 30
DSolve[2*x^2*y''[x]-3*x*y'[x]+2*y[x]==Log[x^2],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} \left (\log \left (x^2\right )+5\right )+c_2 x^2+c_1 \sqrt {x} \]