83.49.2 problem Ex 2 page 120

Internal problem ID [19615]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter VIII. Linear equations of second order
Problem number : Ex 2 page 120
Date solved : Tuesday, January 28, 2025 at 08:32:59 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.210 (sec). Leaf size: 29

dsolve(sin(x)^2*diff(y(x),x$2)=2*y(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.143 (sec). Leaf size: 55

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

\[ y(x)\to \frac {c_2 \cos (x) \text {arctanh}\left (\frac {\cos (x)}{\sqrt {-\sin ^2(x)}}\right )+c_1 \cos (x)-c_2 \sqrt {-\sin ^2(x)}}{\sqrt {-\sin ^2(x)}} \]