60.3.272 problem 1277

Internal problem ID [11282]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1277
Date solved : Monday, January 27, 2025 at 11:05:02 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.089 (sec). Leaf size: 27

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

\[ y = \frac {c_{1} \sinh \left (\frac {\sqrt {a}\, x}{2}\right )+c_{2} \cosh \left (\frac {\sqrt {a}\, x}{2}\right )}{\sqrt {x}} \]

✓ Solution by Mathematica

Time used: 0.055 (sec). Leaf size: 49

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

\[ y(x)\to \frac {e^{-\frac {\sqrt {a} x}{2}} \left (c_2 e^{\sqrt {a} x}+\sqrt {a} c_1\right )}{\sqrt {a} \sqrt {x}} \]