Internal problem ID [5268]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary
problems. Page 33
Problem number: 23 (k).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
\[ \boxed {x \sqrt {x^{2}+y^{2}}-y+\left (y \sqrt {x^{2}+y^{2}}-x \right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve((x*sqrt(x^2+y(x)^2)-y(x))+(y(x)*sqrt(x^2+y(x)^2)-x)*diff(y(x),x)=0,y(x), singsol=all)
\[ \frac {\left (x^{2}+y^{2}\right )^{\frac {3}{2}}}{3}-y x +c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 30.753 (sec). Leaf size: 319
DSolve[(x*Sqrt[x^2+y[x]^2]-y[x])+(y[x]*Sqrt[x^2+y[x]^2]-x)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {Root}\left [\text {$\#$1}^6+3 \text {$\#$1}^4 x^2+\text {$\#$1}^2 \left (3 x^4-9 x^2\right )-18 \text {$\#$1} c_1 x+x^6-9 c_1{}^2\&,1\right ] y(x)\to \text {Root}\left [\text {$\#$1}^6+3 \text {$\#$1}^4 x^2+\text {$\#$1}^2 \left (3 x^4-9 x^2\right )-18 \text {$\#$1} c_1 x+x^6-9 c_1{}^2\&,2\right ] y(x)\to \text {Root}\left [\text {$\#$1}^6+3 \text {$\#$1}^4 x^2+\text {$\#$1}^2 \left (3 x^4-9 x^2\right )-18 \text {$\#$1} c_1 x+x^6-9 c_1{}^2\&,3\right ] y(x)\to \text {Root}\left [\text {$\#$1}^6+3 \text {$\#$1}^4 x^2+\text {$\#$1}^2 \left (3 x^4-9 x^2\right )-18 \text {$\#$1} c_1 x+x^6-9 c_1{}^2\&,4\right ] y(x)\to \text {Root}\left [\text {$\#$1}^6+3 \text {$\#$1}^4 x^2+\text {$\#$1}^2 \left (3 x^4-9 x^2\right )-18 \text {$\#$1} c_1 x+x^6-9 c_1{}^2\&,5\right ] y(x)\to \text {Root}\left [\text {$\#$1}^6+3 \text {$\#$1}^4 x^2+\text {$\#$1}^2 \left (3 x^4-9 x^2\right )-18 \text {$\#$1} c_1 x+x^6-9 c_1{}^2\&,6\right ] \end{align*}