83.19.8 problem 8

Internal problem ID [19236]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter IV. Equations of the first order but not of the first degree. Exercise IV (B) at page 55
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 01:15:14 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.033 (sec). Leaf size: 32

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

\begin{align*} y \left (x \right ) &= 0 \\ x -\int _{}^{y \left (x \right )}\frac {1}{\operatorname {RootOf}\left (\textit {\_a} -\sin \left (\textit {\_Z} \right )+\textit {\_Z} \cos \left (\textit {\_Z} \right )\right )}d \textit {\_a} -c_{1} &= 0 \\ \end{align*}

✓ Solution by Mathematica

Time used: 5.193 (sec). Leaf size: 174

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

\begin{align*} y(x)\to (x-c_1) \arccos (-x+c_1)-\sqrt {-x^2+2 c_1 x+1-c_1{}^2} \\ y(x)\to (-x+c_1) \arccos (-x+c_1)-\sqrt {-x^2+2 c_1 x+1-c_1{}^2} \\ y(x)\to (x-c_1) \arccos (-x+c_1)+\sqrt {-x^2+2 c_1 x+1-c_1{}^2} \\ y(x)\to (-x+c_1) \arccos (-x+c_1)+\sqrt {-x^2+2 c_1 x+1-c_1{}^2} \\ y(x)\to 0 \\ \end{align*}