36.3.17 problem 18

Internal problem ID [6338]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.4, Exact equations. Exercises. page 64
Problem number : 18
Date solved : Monday, January 27, 2025 at 01:56:54 PM
CAS classification : [_exact]

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 40

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

\[ y = -x +\operatorname {RootOf}\left (-\sin \left (\textit {\_Z} \right )+x^{3}-2 x^{2} \textit {\_Z} +x \,\textit {\_Z}^{2}+x^{2}-{\mathrm e}^{-x +\textit {\_Z}}+c_1 \right ) \]

✓ Solution by Mathematica

Time used: 0.449 (sec). Leaf size: 36

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

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