59.1.455 problem 469

Internal problem ID [9627]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 469
Date solved : Monday, January 27, 2025 at 06:04:47 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 14

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

\[ y = {\mathrm e}^{x} \left (c_{2} x^{3}+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.062 (sec). Leaf size: 31

DSolve[x*D[y[x],{x,2}]-(2*x+2)*D[y[x],x]+(x+2)*y[x]==6*x^3*Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{6} e^x \left (9 x^4+2 e c_2 x^3+6 e c_1\right ) \]