60.3.219 problem 1223

Internal problem ID [11229]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1223
Date solved : Monday, January 27, 2025 at 10:49:21 PM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }-9 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 23

dsolve((x^2+1)*diff(diff(y(x),x),x)+x*diff(y(x),x)-9*y(x)=0,y(x), singsol=all)
 

\[ y = c_{2} \cosh \left (3 \,\operatorname {arcsinh}\left (x \right )\right )+\left (4 x^{3}+3 x \right ) c_{1} \]

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 25

DSolve[-9*y[x] + x*D[y[x],x] + (1 + x^2)*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \cosh (3 \text {arcsinh}(x))+i c_2 \sinh (3 \text {arcsinh}(x)) \]