20.5.11 problem Problem 11

Internal problem ID [3694]
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
Date solved : Monday, January 27, 2025 at 07:55:28 AM
CAS classification : [_exact]

\begin{align*} y^{2}+\cos \left (x \right )+\left (2 y x +\sin \left (y\right )\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.028 (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)
 

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

✓ Solution by Mathematica

Time used: 0.227 (sec). Leaf size: 20

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

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