83.27.13 problem 13

Internal problem ID [19359]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Exercise VII (A) at page 104
Problem number : 13
Date solved : Tuesday, January 28, 2025 at 01:35:24 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} \sin \left (x \right ) y^{\prime \prime }-\cos \left (x \right ) y^{\prime }+2 y \sin \left (x \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.063 (sec). Leaf size: 39

dsolve(sin(x)*diff(y(x),x$2)-cos(x)*diff(y(x),x)+2*y(x)*sin(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = -\ln \left (-1+\cos \left (x \right )\right ) c_{2} \sin \left (x \right )^{2}+\ln \left (1+\cos \left (x \right )\right ) c_{2} \sin \left (x \right )^{2}+c_{1} \sin \left (x \right )^{2}+2 c_{2} \cos \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.102 (sec). Leaf size: 45

DSolve[Sin[x]*D[y[x],{x,2}]-Cos[x]*D[y[x],x]+2*y[x]*Sin[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -c_1 \sin ^2(x)-\frac {1}{4} c_2 \left (2 \cos (x)+\sin ^2(x) (\log (\cos (x)+1)-\log (1-\cos (x)))\right ) \]