73.16.9 problem 24.1 (i)

Internal problem ID [15521]
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)
Date solved : Tuesday, January 28, 2025 at 08:01:00 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=x^{2} \end{align*}

✓ Solution by Maple

Time used: 0.006 (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)
 

\[ y = x^{2} \left (c_{2} +\ln \left (x \right ) c_{1} +\frac {\ln \left (x \right )^{2}}{2}\right ) \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 27

DSolve[x^2*D[y[x],{x,2}]-3*x*D[y[x],x]+4*y[x]==x^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} x^2 \left (\log ^2(x)+4 c_2 \log (x)+2 c_1\right ) \]