83.37.8 problem 8

Internal problem ID [19453]
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 (B) at page 128
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 01:44:36 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+5 y&=\sec \left (x \right ) {\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 29

dsolve(diff(y(x),x$2)-2*tan(x)*diff(y(x),x)+5*y(x)=sec(x)*exp(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\sec \left (x \right ) \left (7 \sin \left (\sqrt {6}\, x \right ) c_{2} +7 \cos \left (\sqrt {6}\, x \right ) c_{1} +{\mathrm e}^{x}\right )}{7} \]

✓ Solution by Mathematica

Time used: 0.204 (sec). Leaf size: 56

DSolve[D[y[x],{x,2}]-2*Tan[x]*D[y[x],x]+5*y[x]==Sec[x]*Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{84} \left (12 e^x+84 c_1 e^{-i \sqrt {6} x}-7 i \sqrt {6} c_2 e^{i \sqrt {6} x}\right ) \sec (x) \]