60.1.275 problem 276

Internal problem ID [10289]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 276
Date solved : Monday, January 27, 2025 at 06:50:31 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 47

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

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

✓ Solution by Mathematica

Time used: 0.131 (sec). Leaf size: 44

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

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