Internal problem ID [6465]
Book: Own collection of miscellaneous problems
Section: section 3.0
Problem number: 29.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class D`]]
\[ \boxed {y^{\prime }-2 x^{2} \sin \left (\frac {y}{x}\right )^{2}-\frac {y}{x}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(diff(y(x),x)= 2*x^2 * sin(y(x)/x)^2 + y(x)/x,y(x), singsol=all)
\[ y \left (x \right ) = -\left (-\pi +\operatorname {arccot}\left (x^{2}+2 c_{1} \right )\right ) x \]
✓ Solution by Mathematica
Time used: 0.313 (sec). Leaf size: 22
DSolve[y'[x]== 2*x^2 * Sin[y[x]/x]^2 + y[x]/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x \cot ^{-1}\left (x^2-2 c_1\right ) \\ y(x)\to 0 \\ \end{align*}