Internal problem ID [13157]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 13. Higher order equations: Extending first order concepts. Additional exercises
page 259
Problem number: 13.1 (e).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {x y^{\prime \prime }-y^{\prime }+2 y^{\prime } x^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve(x*diff(y(x),x$2)=diff(y(x),x)-2*x^2*diff(y(x),x),y(x), singsol=all)
\[ y \left (x \right ) = c_{1} +{\mathrm e}^{-x^{2}} c_{2} \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 21
DSolve[x*y''[x]==y'[x]-2*x^2*y'[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2-\frac {1}{2} c_1 e^{-x^2} \]