83.37.12 problem 12

Internal problem ID [19457]
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 : 12
Date solved : Tuesday, January 28, 2025 at 01:44:59 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {y \left (-8+\sqrt {x}+x \right )}{4 x^{2}}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 19

dsolve(diff(y(x),x$2)-1/sqrt(x)*diff(y(x),x)+y(x)/(4*x^2)*(-8+sqrt(x)+x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 30

DSolve[D[y[x],{x,2}]-1/Sqrt[x]*D[y[x],x]+y[x]/(4*x^2)*(-8+Sqrt[x]+x)==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^{\sqrt {x}} \left (c_2 x^3+3 c_1\right )}{3 x} \]