Internal problem ID [2106]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-\ln \relax (x ) x^{2}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.01 (sec). Leaf size: 18
dsolve([diff(y(x),x)=x^2*ln(x),y(1) = 2],y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{3} \ln \relax (x )}{3}-\frac {x^{3}}{9}+\frac {19}{9} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 23
DSolve[{y'[x]==x^2*Log[x],{y[1]==2}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{9} \left (-x^3+3 x^3 \log (x)+19\right ) \\ \end{align*}