67.2.20 problem Problem 2(e)

Internal problem ID [13906]
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(e)
Date solved : Monday, March 31, 2025 at 08:17:43 AM
CAS classification : [NONE]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

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