60.1.137 problem 138

Internal problem ID [10151]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 138
Date solved : Monday, January 27, 2025 at 06:30:08 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

\begin{align*} x^{2} y^{\prime }-y^{2}-y x -x^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 11

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

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

✓ Solution by Mathematica

Time used: 0.079 (sec). Leaf size: 29

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

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