Internal problem ID [3100]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 12
Problem number: 352.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [y=_G(x,y')]
Solve \begin {gather*} \boxed {x^{3} y^{\prime }-\cos \relax (y) \left (\cos \relax (y)-2 x^{2} \sin \relax (y)\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 15
dsolve(x^3*diff(y(x),x) = cos(y(x))*(cos(y(x))-2*x^2*sin(y(x))),y(x), singsol=all)
\[ y \relax (x ) = \arctan \left (\frac {\ln \relax (x )-c_{1}}{x^{2}}\right ) \]
✓ Solution by Mathematica
Time used: 7.949 (sec). Leaf size: 75
DSolve[x^3 y'[x]==Cos[y[x]](Cos[y[x]]-2 x^2 Sin[y[x]]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {ArcTan}\left (\frac {\log (x)+4 c_1}{x^2}\right ) \\ y(x)\to -\frac {1}{2} i \left (\log \left (-\frac {4 i}{x^2}\right )-\log \left (\frac {4 i}{x^2}\right )\right ) \\ y(x)\to \frac {1}{2} i \left (\log \left (-\frac {4 i}{x^2}\right )-\log \left (\frac {4 i}{x^2}\right )\right ) \\ \end{align*}