Internal problem ID [3627]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 13
Problem number: 371.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]
\[ \boxed {x^{4} y^{\prime }+y x^{3}+\csc \left (y x \right )=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 27
dsolve(x^4*diff(y(x),x)+x^3*y(x)+csc(x*y(x)) = 0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {-\pi +\arccos \left (\frac {2 c_{1} x^{2}+1}{2 x^{2}}\right )}{x} \]
✓ Solution by Mathematica
Time used: 5.347 (sec). Leaf size: 40
DSolve[x^4 y'[x]+x^3 y[x]+ Csc[x y[x]]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\arccos \left (-\frac {1}{2 x^2}+c_1\right )}{x} y(x)\to \frac {\arccos \left (-\frac {1}{2 x^2}+c_1\right )}{x} \end{align*}