33.3 problem Ex 3

Internal problem ID [10300]

Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section: Chapter IX, Miscellaneous methods for solving equations of higher order than first. Article 57. Dependent variable absent. Page 132
Problem number: Ex 3.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _missing_y]]

Solve \begin {gather*} \boxed {y^{\prime \prime }+y^{\prime } x -x=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 23

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

\[ y \relax (x ) = \frac {c_{1} \sqrt {\pi }\, \sqrt {2}\, \erf \left (\frac {\sqrt {2}\, x}{2}\right )}{2}+x +c_{2} \]

Solution by Mathematica

Time used: 0.092 (sec). Leaf size: 29

DSolve[y''[x]+x*y'[x]==x,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \sqrt {\frac {\pi }{2}} c_1 \text {Erf}\left (\frac {x}{\sqrt {2}}\right )+x+c_2 \\ \end{align*}