3.170 problem 1174

Internal problem ID [9504]

Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1174.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]

\[ \boxed {x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y=x^{5} \ln \left (x \right )} \]

Solution by Maple

Time used: 0.0 (sec). Leaf size: 25

dsolve(x^2*diff(diff(y(x),x),x)-2*x*diff(y(x),x)+2*y(x)-x^5*ln(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {x^{5} \ln \left (x \right )}{12}-\frac {7 x^{5}}{144}+c_{2} x^{2}+c_{1} x \]

Solution by Mathematica

Time used: 0.02 (sec). Leaf size: 32

DSolve[-(x^5*Log[x]) + 2*y[x] - 2*x*y'[x] + x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

\[ y(x)\to -\frac {7 x^5}{144}+\frac {1}{12} x^5 \log (x)+c_2 x^2+c_1 x \]