74.15.22 problem 22

Internal problem ID [16461]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.7, page 195
Problem number : 22
Date solved : Tuesday, January 28, 2025 at 09:08:25 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 20

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

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

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 27

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

\[ y(x)\to \frac {1}{2} x^3 \left (\log ^2(x)+6 c_2 \log (x)+2 c_1\right ) \]