67.2.10 problem Problem 1(j)

Internal problem ID [13888]
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 1(j)
Date solved : Wednesday, March 05, 2025 at 10:21:19 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} \sinh \left (x \right ) {y^{\prime }}^{2}+3 y&=0 \end{align*}

✓ Maple. Time used: 0.172 (sec). Leaf size: 707

ode:=sinh(x)*diff(y(x),x)^2+3*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Mathematica. Time used: 0.359 (sec). Leaf size: 145

ode=Sinh[x]*D[y[x],x]^2+3*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to 3 i \operatorname {EllipticF}\left (\frac {1}{4} (\pi -2 i x),2\right )^2-\sqrt {3} c_1 \sqrt {i \sinh (x)} \sqrt {\text {csch}(x)} \operatorname {EllipticF}\left (\frac {1}{4} (\pi -2 i x),2\right )+\frac {c_1{}^2}{4} \\ y(x)\to 3 i \operatorname {EllipticF}\left (\frac {1}{4} (\pi -2 i x),2\right )^2+\sqrt {3} c_1 \sqrt {i \sinh (x)} \sqrt {\text {csch}(x)} \operatorname {EllipticF}\left (\frac {1}{4} (\pi -2 i x),2\right )+\frac {c_1{}^2}{4} \\ y(x)\to 0 \\ \end{align*}

✗ Sympy

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

Timed Out