29.13.17 problem 371

Internal problem ID [4971]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 13
Problem number : 371
Date solved : Monday, January 27, 2025 at 10:00:21 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} x^{4} y^{\prime }+x^{3} y+\csc \left (y x \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.102 (sec). Leaf size: 26

dsolve(x^4*diff(y(x),x)+x^3*y(x)+csc(x*y(x)) = 0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\frac {\pi }{2}+\arcsin \left (\frac {2 c_{1} x^{2}+1}{2 x^{2}}\right )}{x} \]

✓ Solution by Mathematica

Time used: 4.788 (sec). Leaf size: 40

DSolve[x^4 D[y[x],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*}