8.12 problem 12

Internal problem ID [4367]

Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section: Chapter 8, Ordinary differential equations. Section 13. Miscellaneous problems. page 466
Problem number: 12.
ODE order: 2.
ODE degree: 1.

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

Solve \begin {gather*} \boxed {x y^{\prime \prime }+y^{\prime }-4 x=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 13

dsolve(x*diff(y(x),x$2)+diff(y(x),x)=4*x,y(x), singsol=all)
 

\[ y \relax (x ) = x^{2}+c_{1} \ln \relax (x )+c_{2} \]

Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 16

DSolve[x*y''[x]+y'[x]==4*x,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to x^2+c_1 \log (x)+c_2 \\ \end{align*}