20.1.35 problem Problem 47

Internal problem ID [3592]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.2, Basic Ideas and Terminology. page 21
Problem number : Problem 47
Date solved : Monday, January 27, 2025 at 07:46:53 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 20

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)
 

\[ y \left (x \right ) = x^{2} \left (c_{2} +\ln \left (x \right ) c_{1} +\frac {\ln \left (x \right )^{3}}{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 27

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]
 

\[ y(x)\to \frac {1}{6} x^2 \left (\log ^3(x)+12 c_2 \log (x)+6 c_1\right ) \]