83.49.11 problem Ex 11 page 127

Internal problem ID [19624]
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 11 page 127
Date solved : Tuesday, January 28, 2025 at 02:05:00 PM
CAS classification : [_Lienard]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 24

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

\[ y \left (x \right ) = \sec \left (x \right ) \left (c_{1} \sin \left (\sqrt {2}\, x \right )+c_{2} \cos \left (\sqrt {2}\, x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.078 (sec). Leaf size: 51

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

\[ y(x)\to \frac {1}{4} e^{-i \sqrt {2} x} \left (4 c_1-i \sqrt {2} c_2 e^{2 i \sqrt {2} x}\right ) \sec (x) \]