56.5.20 problem 20

Internal problem ID [8981]
Book : Own collection of miscellaneous problems
Section : section 5.0
Problem number : 20
Date solved : Monday, January 27, 2025 at 05:26:11 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 23

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

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