74.10.43 problem 42 (a)

Internal problem ID [16248]
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 (a)
Date solved : Tuesday, January 28, 2025 at 08:25:46 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} {y^{\prime \prime }}^{2}-5 y^{\prime \prime } y^{\prime }+4 y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.432 (sec). Leaf size: 85

dsolve(diff(y(t),t$2)^2-5*diff(y(t),t$2)*diff(y(t),t)+4*y(t)^2=0,y(t), singsol=all)
 

\begin{align*} y &= 0 \\ y &= {\mathrm e}^{\int \operatorname {RootOf}\left (t +2 \left (\int _{}^{\textit {\_Z}}\frac {1}{2 \textit {\_f}^{2}+\sqrt {25 \textit {\_f}^{2}-16}-5 \textit {\_f}}d \textit {\_f} \right )+c_{1} \right )d t +c_{2}} \\ y &= {\mathrm e}^{\int \operatorname {RootOf}\left (t -2 \left (\int _{}^{\textit {\_Z}}-\frac {1}{2 \textit {\_f}^{2}-\sqrt {25 \textit {\_f}^{2}-16}-5 \textit {\_f}}d \textit {\_f} \right )+c_{1} \right )d t +c_{2}} \\ \end{align*}

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[D[y[t],{t,2}]^2-5*D[y[t],{t,2}]*D[y[t],t]+4*y[t]^2==0,y[t],t,IncludeSingularSolutions -> True]
 

Not solved