20.10.4 problem Problem 17

Internal problem ID [3776]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.8, A Differential Equation with Nonconstant Coefficients. page 567
Problem number : Problem 17
Date solved : Monday, January 27, 2025 at 08:01:26 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+5 y&=8 x \ln \left (x \right )^{2} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 28

dsolve(x^2*diff(y(x),x$2)-x*diff(y(x),x)+5*y(x)=8*x*(ln(x))^2,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.146 (sec). Leaf size: 31

DSolve[x^2*D[y[x],{x,2}]-x*D[y[x],x]+5*y[x]==8*x*(Log[x])^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x \left (2 \log ^2(x)+c_2 \cos (2 \log (x))+c_1 \sin (2 \log (x))-1\right ) \]