5.11 problem Problem 11

Internal problem ID [2214]

Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section: Chapter 1, First-Order Differential Equations. Section 1.9, Exact Differential Equations. page 91
Problem number: Problem 11.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_exact]

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

Solution by Maple

Time used: 0.032 (sec). Leaf size: 18

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

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

Solution by Mathematica

Time used: 0.206 (sec). Leaf size: 20

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

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