20.10.7 problem Problem 20

Internal problem ID [3779]
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 20
Date solved : Monday, January 27, 2025 at 08:02:04 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=\frac {x^{2}}{\ln \left (x \right )} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 22

dsolve(x^2*diff(y(x),x$2)-3*x*diff(y(x),x)+4*y(x)=x^2/ln(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 24

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

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