Internal problem ID [5248]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 4. Equations of first order and first degree (Variable separable). Supplemetary
problems. Page 22
Problem number: 38.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {2 x y^{\prime }-2 y-\sqrt {x^{2}+4 y^{2}}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 30
dsolve(2*x*diff(y(x),x)-2*y(x)= sqrt(x^2+4*y(x)^2),y(x), singsol=all)
\[ \frac {-c_{1} x^{2}+2 y \left (x \right )+\sqrt {x^{2}+4 y \left (x \right )^{2}}}{x^{2}} = 0 \]
✓ Solution by Mathematica
Time used: 0.394 (sec). Leaf size: 27
DSolve[2*x*y'[x]-2*y[x]== Sqrt[x^2+4*y[x]^2],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} e^{-2 c_1} \left (-1+e^{4 c_1} x^2\right ) \]