73.17.7 problem 7

Internal problem ID [15541]
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 : 7
Date solved : Tuesday, January 28, 2025 at 08:01:37 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} 2 x y^{\prime \prime }+y^{\prime }&=\sqrt {x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 16

dsolve(2*x*diff(y(x),x$2)+diff(y(x),x)=sqrt(x),y(x), singsol=all)
 

\[ y = \frac {\sqrt {x}\, \left (x +6 c_{1} \right )}{3}+c_{2} \]

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 23

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

\[ y(x)\to \frac {1}{3} \sqrt {x} (x+6 c_1)+c_2 \]