83.19.9 problem 9

Internal problem ID [19237]
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 : 9
Date solved : Tuesday, January 28, 2025 at 01:15:17 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 34

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

\[ y \left (x \right ) = \frac {2 \cot \left (x \right )-\pi +2 \csc \left (x \right )+2 x +2 c_{1}}{2 \csc \left (x \right )+2 \cot \left (x \right )} \]

✓ Solution by Mathematica

Time used: 0.159 (sec). Leaf size: 44

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

\[ y(x)\to \frac {1}{2} e^{-\text {arctanh}(\cos (x))} \left (\sqrt {\sin ^2(x)} \left (\csc ^2\left (\frac {x}{2}\right )+2 x \csc (x)\right )+2 c_1\right ) \]