73.15.80 problem 22.15 (g)

Internal problem ID [15511]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 22. Method of undetermined coefficients. Additional exercises page 412
Problem number : 22.15 (g)
Date solved : Tuesday, January 28, 2025 at 08:00:36 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y&=6 x^{3} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 20

dsolve(x^2*diff(y(x),x$2)-5*x*diff(y(x),x)+9*y(x)=6*x^3,y(x), singsol=all)
 

\[ y = x^{3} \left (c_{2} +\ln \left (x \right ) c_{1} +3 \ln \left (x \right )^{2}\right ) \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 24

DSolve[x^2*D[y[x],{x,2}]-5*x*D[y[x],x]+9*y[x]==6*x^3,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^3 \left (3 \log ^2(x)+3 c_2 \log (x)+c_1\right ) \]