59.1.670 problem 687

Internal problem ID [9842]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 687
Date solved : Monday, January 27, 2025 at 06:14:56 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 48

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

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

✓ Solution by Mathematica

Time used: 0.192 (sec). Leaf size: 45

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

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