62.33.3 problem Ex 3

Internal problem ID [12990]
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
Date solved : Tuesday, January 28, 2025 at 04:46:28 AM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 23

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

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

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 29

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

\[ y(x)\to \sqrt {\frac {\pi }{2}} c_1 \text {erf}\left (\frac {x}{\sqrt {2}}\right )+x+c_2 \]