59.1.173 problem 175

Internal problem ID [9345]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 175
Date solved : Monday, January 27, 2025 at 06:01:43 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-3 \left (x +3\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 50

dsolve(x^2*diff(y(x),x$2)+x*(1+x)*diff(y(x),x)-3*(3+x)*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {-c_{2} \left (x^{5}-x^{4}+2 x^{3}-6 x^{2}+24 x -120\right ) {\mathrm e}^{-x}+x^{6} \left (\operatorname {Ei}_{1}\left (x \right ) c_{2} +c_{1} \right )}{x^{3}} \]

✓ Solution by Mathematica

Time used: 0.367 (sec). Leaf size: 40

DSolve[x^2*D[y[x],{x,2}]+x*(1+x)*D[y[x],x]-3*(3+x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{7/2} x^3 \left (c_2 \int _1^x\frac {e^{-K[1]-7}}{K[1]^7}dK[1]+c_1\right ) \]