8.5.37 problem 37

Internal problem ID [765]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.6, Substitution methods and exact equations. Page 74
Problem number : 37
Date solved : Monday, January 27, 2025 at 03:04:12 AM
CAS classification : [_exact]

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

✓ Solution by Maple

Time used: 0.097 (sec). Leaf size: 24

dsolve(cos(x)+ln(y(x))+(exp(y(x))+x/y(x))*diff(y(x),x) = 0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.348 (sec). Leaf size: 18

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

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