50.4.16 problem 16

Internal problem ID [7865]
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
Date solved : Monday, January 27, 2025 at 03:28:07 PM
CAS classification : [_exact]

\begin{align*} {\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 \end{align*}

✓ Solution by Maple

Time used: 0.885 (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)
 

\[ \csc \left (y\right ) \cot \left (x \right )+x \,{\mathrm e}^{y^{2}}+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 148.303 (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])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [-2 x e^{y(x)^2}-2 \cot (x) \csc (y(x))=c_1,y(x)\right ] \]