82.48.10 problem Ex. 10

Internal problem ID [18991]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VIII. End of chapter problems at page 107
Problem number : Ex. 10
Date solved : Tuesday, January 28, 2025 at 12:44:40 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

✓ Solution by Maple

Time used: 0.055 (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: 0.101 (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]
 

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