83.49.10 problem Ex 10 page 127

Internal problem ID [19623]
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 10 page 127
Date solved : Tuesday, January 28, 2025 at 02:04:58 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x^{{1}/{3}}}+\left (\frac {1}{4 x^{{2}/{3}}}-\frac {1}{6 x^{{4}/{3}}}-\frac {6}{x^{2}}\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 21

dsolve(diff(y(x),x$2)+1/x^(1/3)*diff(y(x),x)+(1/(4*x^(2/3))-1/(6*x^(4/3))-6/x^2)*y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {{\mathrm e}^{-\frac {3 x^{{2}/{3}}}{4}} \left (c_{2} x^{5}+c_{1} \right )}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.045 (sec). Leaf size: 34

DSolve[D[y[x],{x,2}]+1/x^(1/3)*D[y[x],x]+(1/(4*x^(2/3))-1/(6*x^(4/3))-6/x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^{-\frac {3 x^{2/3}}{4}} \left (c_2 x^5+5 c_1\right )}{5 x^2} \]