3.129 problem 1133

Internal problem ID [9463]

Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1133.
ODE order: 2.
ODE degree: 1.

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

\[ \boxed {\left (2 x -1\right ) y^{\prime \prime }-\left (3 x -4\right ) y^{\prime }+\left (x -3\right ) y=0} \]

Solution by Maple

Time used: 0.078 (sec). Leaf size: 31

dsolve((2*x-1)*diff(diff(y(x),x),x)-(3*x-4)*diff(y(x),x)+(x-3)*y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {{\mathrm e}^{-\frac {1}{4}+x} \sqrt {2}\, \left (\left (\frac {c_{1}}{4}+c_{2} \right ) \Gamma \left (-\frac {1}{4}, -\frac {1}{4}+\frac {x}{2}\right )+\Gamma \left (\frac {3}{4}\right ) c_{1} \right )}{2} \]

Solution by Mathematica

Time used: 0.253 (sec). Leaf size: 47

DSolve[(-3 + x)*y[x] - (-4 + 3*x)*y'[x] + (-1 + 2*x)*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

\[ y(x)\to -\frac {e^{x-\frac {1}{2}} \left (\sqrt [4]{2} c_2 \Gamma \left (-\frac {1}{4},\frac {1}{4} (2 x-1)\right )-8 c_1\right )}{4\ 2^{3/8}} \]