Internal problem ID [3189]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class D`]]
\[ \boxed {y-2 x^{3} \tan \left (\frac {y}{x}\right )-x y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.015 (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: 59.679 (sec). Leaf size: 23
DSolve[y[x]-2*x^3*Tan[y[x]/x]-x*y'[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*}