73.16.1 problem 24.1 (a)

Internal problem ID [15513]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 24. Variation of parameters. Additional exercises page 444
Problem number : 24.1 (a)
Date solved : Tuesday, January 28, 2025 at 08:00:40 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 18

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

\[ y = c_{2} x^{2}+c_{1} x +4 \sqrt {x} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 23

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

\[ y(x)\to c_2 x^2+4 \sqrt {x}+c_1 x \]