Internal problem ID [5251]
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: 41.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {y^{2}+x y y^{\prime }=x^{2}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 39
dsolve((y(x)^2-x^2)+x*y(x)*diff(y(x),x)= 0,y(x), singsol=all)
\begin{align*} y = -\frac {\sqrt {2 x^{4}+4 c_{1}}}{2 x} y = \frac {\sqrt {2 x^{4}+4 c_{1}}}{2 x} \end{align*}
✓ Solution by Mathematica
Time used: 0.199 (sec). Leaf size: 46
DSolve[(y[x]^2-x^2)+x*y[x]*y'[x]== 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {\frac {x^4}{2}+c_1}}{x} y(x)\to \frac {\sqrt {\frac {x^4}{2}+c_1}}{x} \end{align*}