Internal problem ID [11335]
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 61. Transformation of variables. Page 143
Problem number: Ex 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\sin \left (x \right )^{2} y^{\prime \prime }-2 y=0} \]
✓ Solution by Maple
Time used: 0.344 (sec). Leaf size: 31
dsolve(sin(x)^2*diff(y(x),x$2)-2*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = -i \cot \left (x \right ) \ln \left (\cos \left (2 x \right )+i \sin \left (2 x \right )\right ) c_{2} -2 c_{2} +c_{1} \cot \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.339 (sec). Leaf size: 46
DSolve[Sin[x]^2*y''[x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\cos (x) \left (c_1-c_2 \log \left (\sqrt {-\sin ^2(x)}-\cos (x)\right )\right )}{\sqrt {-\sin ^2(x)}}-c_2 \]