Internal problem ID [5407]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 17. Linear equations with variable coefficients (Cauchy and Legndre).
Supplemetary problems. Page 110
Problem number: 7.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y=\ln \left (x \right )^{2}-\ln \left (x^{2}\right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve(x^2*diff(y(x),x$2)-2*x*diff(y(x),x)+2*y(x)=(ln(x))^2-ln(x^2),y(x), singsol=all)
\[ y = c_{2} x^{2}+c_{1} x +\frac {\ln \left (x \right )^{2}}{2}+\frac {3 \ln \left (x \right )}{2}-\frac {\ln \left (x^{2}\right )}{2}+\frac {1}{4} \]
✓ Solution by Mathematica
Time used: 0.032 (sec). Leaf size: 38
DSolve[x^2*y''[x]-2*x*y'[x]+2*y[x]==(Log[x])^2-Log[x^2],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} \left (-2 \log \left (x^2\right )+2 \log ^2(x)+6 \log (x)+1\right )+c_2 x^2+c_1 x \]