Internal problem ID [118]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.6, Substitution methods and exact equations. Page 74
Problem number: 40.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
Solve \begin {gather*} \boxed {{\mathrm e}^{x} \sin \relax (y)+\tan \relax (y)+\left ({\mathrm e}^{x} \cos \relax (y)+x \left (\sec ^{2}\relax (y)\right )\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 153
dsolve(exp(x)*sin(y(x))+tan(y(x))+(exp(x)*cos(y(x))+x*sec(y(x))^2)*diff(y(x),x) = 0,y(x), singsol=all)
\[ y \relax (x ) = \arctan \left (-\frac {c_{1} \RootOf \left (\textit {\_Z}^{4} {\mathrm e}^{2 x}+2 x \,{\mathrm e}^{x} \textit {\_Z}^{3}+\left (c_{1}^{2}+x^{2}-{\mathrm e}^{2 x}\right ) \textit {\_Z}^{2}-2 x \,{\mathrm e}^{x} \textit {\_Z} -x^{2}\right )}{\RootOf \left (\textit {\_Z}^{4} {\mathrm e}^{2 x}+2 x \,{\mathrm e}^{x} \textit {\_Z}^{3}+\left (c_{1}^{2}+x^{2}-{\mathrm e}^{2 x}\right ) \textit {\_Z}^{2}-2 x \,{\mathrm e}^{x} \textit {\_Z} -x^{2}\right ) {\mathrm e}^{x}+x}, \RootOf \left (\textit {\_Z}^{4} {\mathrm e}^{2 x}+2 x \,{\mathrm e}^{x} \textit {\_Z}^{3}+\left (c_{1}^{2}+x^{2}-{\mathrm e}^{2 x}\right ) \textit {\_Z}^{2}-2 x \,{\mathrm e}^{x} \textit {\_Z} -x^{2}\right )\right ) \]
✓ Solution by Mathematica
Time used: 60.841 (sec). Leaf size: 5539
DSolve[Exp[x]*Sin[y[x]]+Tan[y[x]]+(Exp[x]*Cos[y[x]]+x*Sec[y[x]]^2)*y'[x] == 0,y[x],x,IncludeSingularSolutions -> True]
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