Internal problem ID [4334]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 7. Other second-Order equations. page
435
Problem number: 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime } x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 10
dsolve(diff(y(x),x$2)+2*x*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} +\operatorname {erf}\left (x \right ) c_{2} \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 21
DSolve[y''[x]+2*x*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \sqrt {\pi } c_1 \text {erf}(x)+c_2 \\ \end{align*}