60.1.110 problem 110

Internal problem ID [10124]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 110
Date solved : Monday, January 27, 2025 at 06:28:32 PM
CAS classification : [[_homogeneous, `class D`], _Riccati]

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

✓ Solution by Maple

Time used: 0.037 (sec). Leaf size: 13

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

\[ y = \tanh \left (\int fd x +c_{1} \right ) x \]

✓ Solution by Mathematica

Time used: 0.108 (sec). Leaf size: 44

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

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {1}{(K[1]-1) (K[1]+1)}dK[1]=\int _1^x-f(K[2])dK[2]+c_1,y(x)\right ] \]