60.1.185 problem 186

Internal problem ID [10199]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 186
Date solved : Monday, January 27, 2025 at 06:37:41 PM
CAS classification : [[_homogeneous, `class G`], _Riccati]

\begin{align*} x^{n} y^{\prime }+y^{2}-\left (n -1\right ) x^{n -1} y+x^{2 n -2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.676 (sec). Leaf size: 19

DSolve[x^n*D[y[x],x] + y[x]^2 -(n-1)*x^(n-1)*y[x] + x^(2*n-2)==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^{n-1} \tan (-\log (x)+c_1) \]