Internal problem ID [14046]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [`y=_G(x,y')`]
\[ \boxed {y y^{\prime }+y^{4}=\sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 164
dsolve(y(x)*diff(y(x),x)+y(x)^4=sin(x),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -\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 \left (x \right ) &= \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: 0.0 (sec). Leaf size: 0
DSolve[y[x]*y'[x]+y[x]^4==Sin[x],y[x],x,IncludeSingularSolutions -> True]
Not solved