Internal problem ID [3455]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 7
Problem number: 199.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [`y=_G(x,y')`]
\[ \boxed {x y^{\prime }+\left (\sin \left (y\right )-3 \cos \left (y\right ) x^{2}\right ) \cos \left (y\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(x*diff(y(x),x)+(sin(y(x))-3*x^2*cos(y(x)))*cos(y(x)) = 0,y(x), singsol=all)
\[ y \left (x \right ) = \arctan \left (\frac {x^{3}+2 c_{1}}{x}\right ) \]
✓ Solution by Mathematica
Time used: 1.87 (sec). Leaf size: 53
DSolve[x y'[x]+(Sin[y[x]]-3 x^2 Cos[y[x]]) Cos[y[x]]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \arctan \left (x^2+\frac {c_1}{2 x}\right ) y(x)\to -\frac {1}{2} \pi \sqrt {\frac {1}{x^2}} x y(x)\to \frac {1}{2} \pi \sqrt {\frac {1}{x^2}} x \end{align*}