60.1.106 problem 106

Internal problem ID [10120]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 106
Date solved : Monday, January 27, 2025 at 06:28:21 PM
CAS classification : [_rational, _Riccati]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 39

dsolve(x*diff(y(x),x) + x^a*y(x)^2 + (a-b)*y(x)/2 + x^b=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.649 (sec). Leaf size: 40

DSolve[x*D[y[x],x] + x^a*y[x]^2 + (a-b)*y[x]/2 + x^b==0,y[x],x,IncludeSingularSolutions -> True]
 

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