60.3.276 problem 1281

Internal problem ID [11286]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1281
Date solved : Monday, January 27, 2025 at 11:05:10 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 x^{2} y^{\prime \prime }-4 x \left (2 x -1\right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.046 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.041 (sec). Leaf size: 21

DSolve[(-1 - 4*x + 4*x^2)*y[x] - 4*x*(-1 + 2*x)*D[y[x],x] + 4*x^2*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^x (c_2 x+c_1)}{\sqrt {x}} \]