73.8.5 problem 13.1 (e)

Internal problem ID [15213]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 13. Higher order equations: Extending first order concepts. Additional exercises page 259
Problem number : 13.1 (e)
Date solved : Tuesday, January 28, 2025 at 07:50:06 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} x y^{\prime \prime }&=y^{\prime }-2 x^{2} y^{\prime } \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 14

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

\[ y = c_{1} +c_{2} {\mathrm e}^{-x^{2}} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 21

DSolve[x*D[y[x],{x,2}]==D[y[x],x]-2*x^2*D[y[x],x],y[x],x,IncludeSingularSolutions -> True]
 

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