78.4.15 problem 16

Internal problem ID [18138]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 8 (Exact Equations). Problems at page 72
Problem number : 16
Date solved : Tuesday, January 28, 2025 at 11:31:44 AM
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: 0.040 (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: 147.872 (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]
 

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