Internal problem ID [6197]
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]
\[ \boxed {{\mathrm e}^{y^{2}}-\csc \left (y\right ) \csc \left (x \right )^{2}+\left (2 x y \,{\mathrm e}^{y^{2}}-\csc \left (y\right ) \cot \left (y\right ) \cot \left (x \right )\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.141 (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)
\[ \csc \left (y \left (x \right )\right ) \cot \left (x \right )+x \,{\mathrm e}^{y \left (x \right )^{2}}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 175.525 (sec). Leaf size: 23
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]
\[ \text {Solve}\left [-2 x e^{y(x)^2}-2 \cot (x) \csc (y(x))=c_1,y(x)\right ] \]