Internal problem ID [11357]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter IX, Miscellaneous methods for solving equations of higher order than first.
Article 62. Summary. Page 144
Problem number: Ex 12.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
\[ \boxed {\sin \left (x \right ) y^{\prime \prime }-y^{\prime } \cos \left (x \right )+2 \sin \left (x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.25 (sec). Leaf size: 36
dsolve(sin(x)*diff(y(x),x$2)-cos(x)*diff(y(x),x)+2*sin(x)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (x \right )^{2} c_{1} +c_{2} \sin \left (x \right )^{2} \left (\ln \left (\cos \left (x \right )+1\right )-\ln \left (\cos \left (x \right )-1\right )+2 \csc \left (x \right ) \cot \left (x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.235 (sec). Leaf size: 45
DSolve[Sin[x]*y''[x]-Cos[x]*y'[x]+2*Sin[x]*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -c_1 \sin ^2(x)-\frac {1}{4} c_2 \left (2 \cos (x)+\sin ^2(x) (\log (\cos (x)+1)-\log (1-\cos (x)))\right ) \]