74.1.2 problem 2

Internal problem ID [15711]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number : 2
Date solved : Monday, March 31, 2025 at 01:45:44 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} y y^{\prime }+y^{4}&=\sin \left (x \right ) \end{align*}

✓ Maple. Time used: 0.013 (sec). Leaf size: 164

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

\begin{align*} y &= -\frac {\sqrt {\left (c_1 \operatorname {MathieuC}\left (0, 8, -\frac {\pi }{4}+\frac {x}{2}\right )+\operatorname {MathieuS}\left (0, 8, -\frac {\pi }{4}+\frac {x}{2}\right )\right ) \left (c_1 \operatorname {MathieuCPrime}\left (0, 8, -\frac {\pi }{4}+\frac {x}{2}\right )+\operatorname {MathieuSPrime}\left (0, 8, -\frac {\pi }{4}+\frac {x}{2}\right )\right )}}{2 c_1 \operatorname {MathieuC}\left (0, 8, -\frac {\pi }{4}+\frac {x}{2}\right )+2 \operatorname {MathieuS}\left (0, 8, -\frac {\pi }{4}+\frac {x}{2}\right )} \\ y &= \frac {\sqrt {\left (c_1 \operatorname {MathieuC}\left (0, 8, -\frac {\pi }{4}+\frac {x}{2}\right )+\operatorname {MathieuS}\left (0, 8, -\frac {\pi }{4}+\frac {x}{2}\right )\right ) \left (c_1 \operatorname {MathieuCPrime}\left (0, 8, -\frac {\pi }{4}+\frac {x}{2}\right )+\operatorname {MathieuSPrime}\left (0, 8, -\frac {\pi }{4}+\frac {x}{2}\right )\right )}}{2 c_1 \operatorname {MathieuC}\left (0, 8, -\frac {\pi }{4}+\frac {x}{2}\right )+2 \operatorname {MathieuS}\left (0, 8, -\frac {\pi }{4}+\frac {x}{2}\right )} \\ \end{align*}

✗ Mathematica

ode=y[x]*D[y[x],x]+y[x]^4==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(y(x)**4 + y(x)*Derivative(y(x), x) - sin(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -(-y(x)**4 + sin(x))/y(x) + Derivative(y(x), x) cannot be solved by the factorable group method