20.1.29 problem Problem 37

Internal problem ID [3586]
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 37
Date solved : Monday, January 27, 2025 at 07:46:40 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (1\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 18

dsolve([diff(y(x),x)=x^2*ln(x),y(1) = 2],y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {x^{3} \ln \left (x \right )}{3}-\frac {x^{3}}{9}+\frac {19}{9} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 23

DSolve[{D[y[x],x]==x^2*Log[x],{y[1]==2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{9} \left (-x^3+3 x^3 \log (x)+19\right ) \]