60.1.509 problem 512

Internal problem ID [10523]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 512
Date solved : Monday, January 27, 2025 at 08:48:10 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} \left (a \left (x^{2}+y^{2}\right )^{{3}/{2}}-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+a \left (x^{2}+y^{2}\right )^{{3}/{2}}-y^{2}&=0 \end{align*}

✗ Solution by Maple

dsolve((a*(y(x)^2+x^2)^(3/2)-x^2)*diff(y(x),x)^2+2*x*y(x)*diff(y(x),x)+a*(y(x)^2+x^2)^(3/2)-y(x)^2=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 124.565 (sec). Leaf size: 4537

DSolve[-y[x]^2 + a*(x^2 + y[x]^2)^(3/2) + 2*x*y[x]*D[y[x],x] + (-x^2 + a*(x^2 + y[x]^2)^(3/2))*D[y[x],x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

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