73.17.24 problem 24

Internal problem ID [15558]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 25. Review exercises for part III. page 447
Problem number : 24
Date solved : Tuesday, January 28, 2025 at 08:02:01 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} 2 x^{2} y^{\prime \prime }-3 x y^{\prime }+2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

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

\[ y = c_{1} \sqrt {x}+c_{2} x^{2} \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 20

DSolve[2*x^2*D[y[x],{x,2}]-3*x*D[y[x],x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 x^2+c_1 \sqrt {x} \]