Internal problem ID [10927]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin.
CRC Press 2015
Section: Chapter 4, Second and Higher Order Linear Differential Equations. Problems page
221
Problem number: Problem 20(a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+\frac {2 x y^{\prime }}{2 x -1}-\frac {4 x y}{\left (2 x -1\right )^{2}}=0} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 43
dsolve(diff(y(x),x$2)+ (2*x)/(2*x-1)*diff(y(x),x)- 4*x/( (2*x-1)^2)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} \operatorname {WhittakerM}\left (-\frac {5}{4}, -\frac {3}{4}, x -\frac {1}{2}\right ) {\mathrm e}^{-\frac {x}{2}}}{\left (2 x -1\right )^{\frac {1}{4}}}+\frac {c_{2} \operatorname {WhittakerW}\left (-\frac {5}{4}, -\frac {3}{4}, x -\frac {1}{2}\right ) {\mathrm e}^{-\frac {x}{2}}}{\left (2 x -1\right )^{\frac {1}{4}}} \]
✓ Solution by Mathematica
Time used: 0.131 (sec). Leaf size: 62
DSolve[y''[x]+ (2*x)/(2*x-1)*y'[x]- 4*x/( (2*x-1)^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2 \left (4 e^{\frac {1}{2}-x} (x-1)-(1-2 x)^2 \operatorname {ExpIntegralE}\left (\frac {1}{2},x-\frac {1}{2}\right )\right )}{6 \sqrt {2 x-1}}+c_1 (2 x-1) \\ \end{align*}