60.3.387 problem 1393

Internal problem ID [11397]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1393
Date solved : Tuesday, January 28, 2025 at 06:04:53 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }&=-\frac {\left (b \,x^{2}+c x +d \right ) y}{a \,x^{2} \left (x -1\right )^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.235 (sec). Leaf size: 267

dsolve(diff(diff(y(x),x),x) = -(b*x^2+c*x+d)/a/x^2/(x-1)^2*y(x),y(x), singsol=all)
 

\[ y = \left (x -1\right )^{-\frac {\sqrt {a -4 b -4 c -4 d}-\sqrt {a}}{2 \sqrt {a}}} \left (c_{1} x^{\frac {\sqrt {a -4 d}+\sqrt {a}}{2 \sqrt {a}}} \operatorname {hypergeom}\left (\left [\frac {-\sqrt {a -4 b -4 c -4 d}+\sqrt {a}+\sqrt {a -4 d}+\sqrt {a -4 b}}{2 \sqrt {a}}, \frac {-\sqrt {a -4 b -4 c -4 d}+\sqrt {a}+\sqrt {a -4 d}-\sqrt {a -4 b}}{2 \sqrt {a}}\right ], \left [1+\frac {\sqrt {a -4 d}}{\sqrt {a}}\right ], x\right )+c_{2} x^{-\frac {-\sqrt {a}+\sqrt {a -4 d}}{2 \sqrt {a}}} \operatorname {hypergeom}\left (\left [-\frac {\sqrt {a -4 b -4 c -4 d}-\sqrt {a}+\sqrt {a -4 d}+\sqrt {a -4 b}}{2 \sqrt {a}}, -\frac {\sqrt {a -4 b -4 c -4 d}-\sqrt {a}+\sqrt {a -4 d}-\sqrt {a -4 b}}{2 \sqrt {a}}\right ], \left [1-\frac {\sqrt {a -4 d}}{\sqrt {a}}\right ], x\right )\right ) \]

✓ Solution by Mathematica

Time used: 124.469 (sec). Leaf size: 413606

DSolve[D[y[x],{x,2}] == -(((d + c*x + b*x^2)*y[x])/(a*(-1 + x)^2*x^2)),y[x],x,IncludeSingularSolutions -> True]
 

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