10.5.22 problem 29

Internal problem ID [1214]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.6. Page 100
Problem number : 29
Date solved : Monday, January 27, 2025 at 04:45:27 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} {\mathrm e}^{x}+\left ({\mathrm e}^{x} \cot \left (y\right )+2 \csc \left (y\right ) y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 15

dsolve(exp(x)+(exp(x)*cot(y(x))+2*csc(y(x))*y(x))*diff(y(x),x) = 0,y(x), singsol=all)
 

\[ {\mathrm e}^{x} \sin \left (y\right )+y^{2}+c_1 = 0 \]

✓ Solution by Mathematica

Time used: 0.305 (sec). Leaf size: 18

DSolve[Exp[x]+(Exp[x]*Cot[y[x]]+2*Csc[y[x]]*y[x])*D[y[x],x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [y(x)^2+e^x \sin (y(x))=c_1,y(x)\right ] \]