60.3.284 problem 1289

Internal problem ID [11294]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1289
Date solved : Monday, January 27, 2025 at 11:05:26 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 16 x^{2} y^{\prime \prime }+32 x y^{\prime }-\left (4 x +5\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.098 (sec). Leaf size: 33

dsolve(16*x^2*diff(diff(y(x),x),x)+32*x*diff(y(x),x)-(4*x+5)*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{2} \left (\sqrt {x}+1\right ) {\mathrm e}^{-\sqrt {x}}+c_{1} {\mathrm e}^{\sqrt {x}} \left (\sqrt {x}-1\right )}{x^{{5}/{4}}} \]

✓ Solution by Mathematica

Time used: 0.726 (sec). Leaf size: 65

DSolve[(-5 - 4*x)*y[x] + 32*x*D[y[x],x] + 16*x^2*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^{\sqrt {x}} \left (\sqrt {x}-1\right ) \left (c_2 \int _1^x\frac {e^{-2 \sqrt {K[1]}} \sqrt {K[1]}}{\left (\sqrt {K[1]}-1\right )^2}dK[1]+c_1\right )}{x^{5/4}} \]