Internal problem ID [11324]
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]]
\[ \boxed {y^{\prime \prime }+x y^{\prime }=x} \]
✓ 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)
\[ y \left (x \right ) = \frac {c_{1} \sqrt {\pi }\, \sqrt {2}\, \operatorname {erf}\left (\frac {\sqrt {2}\, x}{2}\right )}{2}+x +c_{2} \]
✓ Solution by Mathematica
Time used: 0.137 (sec). Leaf size: 29
DSolve[y''[x]+x*y'[x]==x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \sqrt {\frac {\pi }{2}} c_1 \text {erf}\left (\frac {x}{\sqrt {2}}\right )+x+c_2 \]