83.38.1 problem 1

Internal problem ID [19460]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VIII. Linear equations of second order. Excercise VIII (C) at page 133
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 01:45:05 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.061 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.055 (sec). Leaf size: 18

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

\[ y(x)\to c_2 \sin (\sin (x))+c_1 \cos (\sin (x)) \]