62.7.3 problem Ex 3

Internal problem ID [12826]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter 2, differential equations of the first order and the first degree. Article 14. Equations reducible to linear equations (Bernoulli). Page 21
Problem number : Ex 3
Date solved : Tuesday, January 28, 2025 at 04:24:59 AM
CAS classification : [_separable]

\begin{align*} \sin \left (y\right ) y^{\prime }+\sin \left (x \right ) \cos \left (y\right )&=\sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.513 (sec). Leaf size: 14

dsolve(sin(y(x))*diff(y(x),x)+sin(x)*cos(y(x))=sin(x),y(x), singsol=all)
 

\[ y = \arccos \left (c_{1} {\mathrm e}^{-\cos \left (x \right )}+1\right ) \]

✓ Solution by Mathematica

Time used: 0.698 (sec). Leaf size: 121

DSolve[Sin[y[x]]*D[y[x],x]+Sin[x]*Cos[y[x]]==Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to 0 \\ \text {Solve}\left [\int _1^x-e^{\text {arctanh}(\cos (y(x)))} \left (\cos \left (K[1]-\frac {y(x)}{2}\right )-\cos \left (K[1]+\frac {y(x)}{2}\right )\right ) \sec \left (\frac {y(x)}{2}\right )dK[1]-y(x) \int _1^x0dK[1]+\sqrt {\sin ^2(y(x))} \left (-\csc \left (\frac {y(x)}{2}\right )\right ) \sec \left (\frac {y(x)}{2}\right ) \left (\log \left (\sec ^2\left (\frac {y(x)}{2}\right )\right )-2 \log \left (\tan \left (\frac {y(x)}{2}\right )\right )\right )&=c_1,y(x)\right ] \\ y(x)\to 0 \\ \end{align*}