Internal problem ID [6466]
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]]
Solve \begin {gather*} \boxed {y^{\prime }-2 x^{2} \left (\sin ^{2}\left (\frac {y}{x}\right )\right )-\frac {y}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 19
dsolve(diff(y(x),x)= 2*x^2 * sin(y(x)/x)^2 + y(x)/x,y(x), singsol=all)
\[ y \relax (x ) = -\left (-\pi +\mathrm {arccot}\left (x^{2}+2 c_{1}\right )\right ) x \]
✓ Solution by Mathematica
Time used: 0.289 (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*}