28.1.44 problem 45

Internal problem ID [4350]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 45
Date solved : Monday, January 27, 2025 at 09:07:45 AM
CAS classification : [[_homogeneous, `class D`]]

\begin{align*} y-2 x^{3} \tan \left (\frac {y}{x}\right )-x y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 15

dsolve(y(x)-2*x^3*tan(y(x)/x)-x*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \arcsin \left (c_{1} {\mathrm e}^{-x^{2}}\right ) x \]

✓ Solution by Mathematica

Time used: 56.981 (sec). Leaf size: 23

DSolve[y[x]-2*x^3*Tan[y[x]/x]-x*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to x \arcsin \left (e^{-x^2+c_1}\right ) \\ y(x)\to 0 \\ \end{align*}