83.49.6 problem Ex 6 page 123

Internal problem ID [19619]
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 6 page 123
Date solved : Tuesday, January 28, 2025 at 02:04:42 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.224 (sec). Leaf size: 51

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

\[ y \left (x \right ) = -\cos \left (x \right ) \left (c_{2} \left (\int {\mathrm e}^{-\int \frac {\cos \left (x \right ) \cot \left (x \right )-2 \sin \left (x \right ) \tan \left (x \right ) x -2 \sin \left (x \right )}{\sin \left (x \right ) x +\cos \left (x \right )}d x} \sin \left (x \right )d x \right )-c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.135 (sec). Leaf size: 16

DSolve[(x*Sin[x]+Cos[x])*D[y[x],{x,2}]-x*Cos[x]*D[y[x],x]+Cos[x]*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 x-c_2 \cos (x) \]