20.3.8 problem Problem 8

Internal problem ID [3617]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.6, First-Order Linear Differential Equations. page 59
Problem number : Problem 8
Date solved : Monday, January 27, 2025 at 07:47:40 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\frac {y}{x \ln \left (x \right )}&=9 x^{2} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 23

dsolve(diff(y(x),x)+1/(x*ln(x))*y(x)=9*x^2,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 25

DSolve[D[y[x],x]+1/(x*Log[x])*y[x]==9*x^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {-x^3+3 x^3 \log (x)+c_1}{\log (x)} \]