Internal problem ID [115]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
\[ \boxed {\ln \left (y\right )+\left ({\mathrm e}^{y}+\frac {x}{y}\right ) y^{\prime }=-\cos \left (x \right )} \]
✓ Solution by Maple
Time used: 0.062 (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)
\[ y \left (x \right ) = {\mathrm e}^{\operatorname {RootOf}\left ({\mathrm e}^{\textit {\_Z}}-\ln \left (-x \textit {\_Z} -c_{1} -\sin \left (x \right )\right )\right )} \]
✓ Solution by Mathematica
Time used: 0.36 (sec). Leaf size: 18
DSolve[Cos[x]+Log[y[x]]+(Exp[y[x]]+x/y[x])*y'[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [e^{y(x)}+x \log (y(x))+\sin (x)=c_1,y(x)\right ] \]