Internal problem ID [14517]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.2, page 147
Problem number: 42 (b).
ODE order: 2.
ODE degree: 2.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {{y^{\prime \prime }}^{2}-2 y^{\prime } y^{\prime \prime }+y^{2}=0} \]
✓ Solution by Maple
Time used: 0.172 (sec). Leaf size: 82
dsolve(diff(y(t),t$2)^2-2*diff(y(t),t$2)*diff(y(t),t)+y(t)^2=0,y(t), singsol=all)
\begin{align*} y \left (t \right ) &= 0 \\ y \left (t \right ) &= {\mathrm e}^{t} c_{1} \\ y \left (t \right ) &= {\mathrm e}^{\int \operatorname {RootOf}\left (t +\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_f}^{2}+\sqrt {\textit {\_f}^{2}-1}-\textit {\_f}}d \textit {\_f} +c_{1} \right )d t +c_{2}} \\ y \left (t \right ) &= {\mathrm e}^{\int \operatorname {RootOf}\left (t -\left (\int _{}^{\textit {\_Z}}-\frac {1}{\textit {\_f}^{2}-\sqrt {\textit {\_f}^{2}-1}-\textit {\_f}}d \textit {\_f} \right )+c_{1} \right )d t +c_{2}} \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y''[t]^2-2*y''[t]*y'[t]+y[t]^2==0,y[t],t,IncludeSingularSolutions -> True]
Not solved