Internal problem ID [13457]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y=3 \sqrt {x}} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y = c_{1} x^{2}+c_{2} x +4 \sqrt {x} \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 23
DSolve[x^2*y''[x]-2*x*y'[x]+2*y[x]==3*Sqrt[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 x^2+4 \sqrt {x}+c_1 x \]