Internal problem ID [5282]
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: 25 (f).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {y^{2}-2 x y y^{\prime }=-3 x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve((3*x^2+y(x)^2)-2*x*y(x)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y = \sqrt {c_{1} x +3 x^{2}} y = -\sqrt {c_{1} x +3 x^{2}} \end{align*}
✓ Solution by Mathematica
Time used: 0.182 (sec). Leaf size: 42
DSolve[(3*x^2+y[x]^2)-2*x*y[x]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {x} \sqrt {3 x+c_1} y(x)\to \sqrt {x} \sqrt {3 x+c_1} \end{align*}