15.5.20 problem 24

Internal problem ID [2956]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 9, page 38
Problem number : 24
Date solved : Monday, January 27, 2025 at 07:00:34 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

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

With initial conditions

\begin{align*} y \left (1\right )&=1 \end{align*}

✗ Solution by Maple

dsolve([(y(x)-x^2*sqrt(x^2-y(x)^2))-x*diff(y(x),x)=0,y(1) = 1],y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[{(y[x]-x^2*Sqrt[x^2-y[x]^2])-x*D[y[x],x]==0,{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
 

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