29.7.6 problem 181

Internal problem ID [4781]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 7
Problem number : 181
Date solved : Monday, January 27, 2025 at 09:37:36 AM
CAS classification : [_rational, _Riccati]

\begin{align*} x y^{\prime }+x^{m}+\frac {\left (n -m \right ) y}{2}+x^{n} y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 39

dsolve(x*diff(y(x),x)+x^m+1/2*(n-m)*y(x)+x^n*y(x)^2 = 0,y(x), singsol=all)
 

\[ y \left (x \right ) = -\tan \left (\frac {2 x^{\frac {n}{2}+\frac {m}{2}}+c_{1} \left (n +m \right )}{n +m}\right ) x^{-\frac {n}{2}+\frac {m}{2}} \]

✓ Solution by Mathematica

Time used: 0.617 (sec). Leaf size: 40

DSolve[x D[y[x],x]+x^m+((n-m)/2) y[x]+x^n y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -x^{\frac {m-n}{2}} \tan \left (\frac {2 x^{\frac {m+n}{2}}}{m+n}-c_1\right ) \]