80.1.8 problem 17 (a)

Internal problem ID [18467]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter 1. section 5. Problems at page 19
Problem number : 17 (a)
Date solved : Monday, March 31, 2025 at 05:30:14 PM
CAS classification : [NONE]

\begin{align*} \sqrt {y^{\prime }+y}&=\left (y^{\prime \prime }+2 x \right )^{{1}/{4}} \end{align*}

✗ Maple

ode:=(diff(y(x),x)+y(x))^(1/2) = (diff(diff(y(x),x),x)+2*x)^(1/4); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=Sqrt[D[y[x],x]+y[x]]== (D[y[x],{x,2}]+2*x)^(1/4); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-(2*x + Derivative(y(x), (x, 2)))**(1/4) + sqrt(y(x) + Derivative(y(x), x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -sqrt(2*x + Derivative(y(x), (x, 2))) + y(x) + Derivative(y(x), x) cannot be solved by the factorable group method