Internal problem ID [13370]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 21. Nonhomogeneous equations in general. Additional exercises page
391
Problem number: 21.14 (b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y=x} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve(x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+6*y(x)=x,y(x), singsol=all)
\[ y = c_{2} x^{2}+c_{1} x^{3}+\frac {1}{2} x \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 23
DSolve[x^2*y''[x]-4*x*y'[x]+6*y[x]==x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 x^3+c_1 x^2+\frac {x}{2} \]