74.1.2 problem 2

Internal problem ID [15782]
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 : Tuesday, January 28, 2025 at 08:25:35 PM
CAS classification : [`y=_G(x,y')`]

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

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 164

dsolve(y(x)*diff(y(x),x)+y(x)^4=sin(x),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*}

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[y[x]*D[y[x],x]+y[x]^4==Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

Not solved