Internal problem ID [6244]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven
Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.9. Reduction of Order. Page
38
Problem number: 2(a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type
[[_2nd_order, _missing_y], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]]
\[ \boxed {\left (x^{2}+2 y^{\prime }\right ) y^{\prime \prime }+2 x y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.079 (sec). Leaf size: 15
dsolve([(x^2+2*diff(y(x),x))*diff(y(x),x$2)+2*x*diff(y(x),x)=0,y(0) = 1, D(y)(0) = 0],y(x), singsol=all)
\begin{align*} y \left (x \right ) &= 1 \\ y \left (x \right ) &= -\frac {x^{3}}{3}+1 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.252 (sec). Leaf size: 32
DSolve[{(x^2+2*y'[x])*y''[x]+2*x*y'[x]==0,{y[0]==1,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {Indeterminate} \\ y(x)\to 0 \operatorname {Hypergeometric2F1}\left (-\frac {1}{2},\frac {1}{4},\frac {5}{4},\text {ComplexInfinity}\right )-\frac {x^3}{6}+1 \\ \end{align*}