44.5.64 problem 54

Internal problem ID [7126]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 54
Date solved : Tuesday, February 04, 2025 at 12:23:14 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.041 (sec). Leaf size: 19

dsolve([diff(y(x),x)=x*arctan(x)/y(x),y(0) = 3],y(x), singsol=all)
 

\[ y = \sqrt {\arctan \left (x \right ) x^{2}+\arctan \left (x \right )-x +9} \]

✓ Solution by Mathematica

Time used: 0.144 (sec). Leaf size: 22

DSolve[{D[y[x],x]==x*ArcTan[x]/y[x],{y[0]==3}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sqrt {x^2 \arctan (x)+\arctan (x)-x+9} \]