4.12 problem 12

Internal problem ID [5440]

Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.5. Exact Equations. Page 20
Problem number: 12.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_exact]

Solve \begin {gather*} \boxed {2 x y^{4}+\sin \relax (y)+\left (4 x^{2} y^{3}+x \cos \relax (y)\right ) y^{\prime }=0} \end {gather*}

Solution by Maple

Time used: 0.109 (sec). Leaf size: 18

dsolve((2*x*y(x)^4+sin(y(x)))+(4*x^2*y(x)^3+x*cos(y(x)))*diff(y(x),x)=0,y(x), singsol=all)
 

\[ x^{2} y \relax (x )^{4}+\sin \left (y \relax (x )\right ) x +c_{1} = 0 \]

Solution by Mathematica

Time used: 0.353 (sec). Leaf size: 20

DSolve[(2*x*y[x]^4+Sin[y[x]])+(4*x^2*y[x]^3+x*Cos[y[x]])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [x^2 y(x)^4+x \sin (y(x))=c_1,y(x)\right ] \]