Internal problem ID [15192]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 14. Differential equations admitting of
depression of their order. Exercises page 107
Problem number: 334.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {x y^{\prime \prime }-\left (2 x^{2}+1\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 12
dsolve(x*diff(y(x),x$2)=(1+2*x^2)*diff(y(x),x),y(x), singsol=all)
\[ y = c_{1} +{\mathrm e}^{x^{2}} c_{2} \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 19
DSolve[x*y''[x]==(1+2*x^2)*y'[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_1 e^{x^2}}{2}+c_2 \]