Internal problem ID [2259]
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: 10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y=4 x +\sin \left (\ln \left (x \right )\right )} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 43
dsolve(x^2*diff(y(x),x$2)-2*x*diff(y(x),x)+2*y(x)=4*x+sin(ln(x)),y(x), singsol=all)
\[ y = c_{2} x +c_{1} x^{2}+\frac {\cos \left (\frac {\ln \left (x \right )}{2}\right ) \sin \left (\frac {\ln \left (x \right )}{2}\right )}{5}-4 \ln \left (x \right ) x +\frac {3 \cos \left (\frac {\ln \left (x \right )}{2}\right )^{2}}{5}-4 x -\frac {3}{10} \]
✓ Solution by Mathematica
Time used: 0.071 (sec). Leaf size: 33
DSolve[x^2*y''[x]-2*x*y'[x]+2*y[x]==4*x+Sin[Log[x]],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{10} (\sin (\log (x))+3 \cos (\log (x))+10 x (-4 \log (x)+c_2 x-4+c_1)) \]