83.46.3 problem Ex 3 page 69

Internal problem ID [19568]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter V. Singular solutions
Problem number : Ex 3 page 69
Date solved : Tuesday, January 28, 2025 at 01:57:10 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(y)]`]]

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

✓ Solution by Maple

Time used: 0.840 (sec). Leaf size: 11

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

\[ y \left (x \right ) = -\sin \left (c_{1} \right ) x +c_{1} \]

✓ Solution by Mathematica

Time used: 0.215 (sec). Leaf size: 20

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

\begin{align*} y(x)\to c_1 x-\arcsin (c_1) \\ y(x)\to 0 \\ \end{align*}