Internal problem ID [5444]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.5. Exact Equations. Page
20
Problem number: 16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
Solve \begin {gather*} \boxed {{\mathrm e}^{y^{2}}-\csc \relax (y) \left (\csc ^{2}\relax (x )\right )+\left (2 x y \,{\mathrm e}^{y^{2}}-\csc \relax (y) \cot \relax (y) \cot \relax (x )\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.516 (sec). Leaf size: 18
dsolve((exp(y(x)^2)-csc(y(x))*csc(x)^2)+(2*x*y(x)*exp(y(x)^2)-csc(y(x))*cot(y(x))*cot(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ \cot \relax (x ) \csc \left (y \relax (x )\right )+x \,{\mathrm e}^{y \relax (x )^{2}}+c_{1} = 0 \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[(Exp[y[x]^2]-Csc[y[x]]*Csc[x]^2)+(2*x*y[x]*Exp[y[x]^2]-Csc[y[x]]*Cot[y[x]]*Cot[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
Timed out