68.10.43 problem 42 (a)

Internal problem ID [17535]
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 : Friday, October 03, 2025 at 07:31:34 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.165 (sec). Leaf size: 85

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

\begin{align*} y &= 0 \\ y &= {\mathrm e}^{\int \operatorname {RootOf}\left (t +2 \int _{}^{\textit {\_Z}}\frac {1}{2 \textit {\_f}^{2}+\sqrt {25 \textit {\_f}^{2}-16}-5 \textit {\_f}}d \textit {\_f} +c_1 \right )d t +c_2} \\ y &= {\mathrm e}^{\int \operatorname {RootOf}\left (t -2 \int _{}^{\textit {\_Z}}-\frac {1}{2 \textit {\_f}^{2}-\sqrt {25 \textit {\_f}^{2}-16}-5 \textit {\_f}}d \textit {\_f} +c_1 \right )d t +c_2} \\ \end{align*}

✗ Mathematica

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

Not solved

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(4*y(t)**2 - 5*Derivative(y(t), t)*Derivative(y(t), (t, 2)) + Derivative(y(t), (t, 2))**2,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

NotImplementedError : The given ODE -(4*y(t)**2 + Derivative(y(t), (t, 2))**2)/(5*Derivative(y(t), (t, 2))) + Derivative(y(t), t) cannot be solved by the factorable group method