59.1.56 problem 58

Internal problem ID [9228]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 58
Date solved : Monday, January 27, 2025 at 05:52:18 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-10 x y^{\prime }+28 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 39

dsolve((1+x^2)*diff(y(x),x$2)-10*x*diff(y(x),x)+28*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} +\frac {35}{3} c_{1} x^{4}-14 c_{1} x^{2}+c_{2} x^{7}+21 c_{2} x^{5}-105 c_{2} x^{3}+35 c_{2} x \]

✓ Solution by Mathematica

Time used: 0.352 (sec). Leaf size: 93

DSolve[(1+x^2)*D[y[x],{x,2}]-10*x*D[y[x],x]+28*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to (x+6 i) \left (x^2+1\right )^{5/2} \exp \left (\int _1^x\frac {K[1]+6 i}{K[1]^2+1}dK[1]\right ) \left (c_2 \int _1^x\frac {\exp \left (-2 \int _1^{K[2]}\frac {K[1]+6 i}{K[1]^2+1}dK[1]\right )}{(K[2]+6 i)^2}dK[2]+c_1\right ) \]