Internal problem ID [13785]
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 (i).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y=x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(x^2*diff(y(x),x$2)-3*x*diff(y(x),x)+4*y(x)=x^2,y(x), singsol=all)
\[ y \left (x \right ) = x^{2} \left (c_{2} +c_{1} \ln \left (x \right )+\frac {\ln \left (x \right )^{2}}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 27
DSolve[x^2*y''[x]-3*x*y'[x]+4*y[x]==x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} x^2 \left (\log ^2(x)+4 c_2 \log (x)+2 c_1\right ) \]