3.389 problem 1390

Internal problem ID [8969]

Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1390.
ODE order: 2.
ODE degree: 1.

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

Solve \begin {gather*} \boxed {y^{\prime \prime }+\frac {3 y}{16 x^{2} \left (x -1\right )^{2}}=0} \end {gather*}

Solution by Maple

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

dsolve(diff(diff(y(x),x),x) = -3/16/x^2/(x-1)^2*y(x),y(x), singsol=all)
 

\[ y \relax (x ) = c_{1} \left (x -1\right )^{\frac {1}{4}} x^{\frac {3}{4}}+c_{2} \left (x -1\right )^{\frac {3}{4}} x^{\frac {1}{4}} \]

Solution by Mathematica

Time used: 0.03 (sec). Leaf size: 41

DSolve[y''[x] == (-3*y[x])/(16*(-1 + x)^2*x^2),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to 2 c_2 \sqrt [4]{1-x} x^{3/4}+c_1 (1-x)^{3/4} \sqrt [4]{x} \\ \end{align*}