60.1.280 problem 281

Internal problem ID [10294]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 281
Date solved : Monday, January 27, 2025 at 06:50:52 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 55

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

\begin{align*} y &= \frac {1-\sqrt {-4 c_{1}^{2} x^{2}+4 c_{1} x +1}}{2 c_{1}} \\ y &= \frac {1+\sqrt {-4 c_{1}^{2} x^{2}+4 c_{1} x +1}}{2 c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.177 (sec). Leaf size: 48

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

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