67.2.22 problem Problem 2(h)

Internal problem ID [13908]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 4, Second and Higher Order Linear Differential Equations. Problems page 221
Problem number : Problem 2(h)
Date solved : Monday, March 31, 2025 at 08:17:46 AM
CAS classification : [NONE]

\begin{align*} {y^{\prime \prime \prime }}^{2}+\sqrt {y}&=\sin \left (x \right ) \end{align*}

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],{x,3}]^2+Sqrt[y[x]]==Sin[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(sqrt(y(x)) - sin(x) + Derivative(y(x), (x, 3))**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : solve: Cannot solve sqrt(y(x)) - sin(x) + Derivative(y(x), (x, 3))**2