Internal problem ID [5343]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 6. Existence and uniqueness of solutions to systems and nth order equations. Page
238
Problem number: 1(f).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }-2 y^{\prime }-x^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(x*diff(y(x),x$2)-2*diff(y(x),x)=x^3,y(x), singsol=all)
\[ y \relax (x ) = \frac {1}{4} x^{4}+\frac {1}{3} x^{3} c_{1}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.045 (sec). Leaf size: 24
DSolve[x*y''[x]-2*y'[x]==x^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^4}{4}+\frac {c_1 x^3}{3}+c_2 \\ \end{align*}