90.20.6 problem 6

Internal problem ID [25301]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 5. Second Order Linear Differential Equations. Exercises at page 337
Problem number : 6
Date solved : Thursday, October 02, 2025 at 11:59:46 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+\sqrt {y^{\prime }}+y&=t \end{align*}

✗ Maple

ode:=diff(diff(y(t),t),t)+diff(y(t),t)^(1/2)+y(t) = t; 
dsolve(ode,y(t), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[t],{t,2}]+Sqrt[D[y[t],{t,1}]]+y[t]==t; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

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

NotImplementedError : The given ODE -(-t + y(t) + Derivative(y(t), (t, 2)))**2 + Derivative(y(t), t)