Internal problem ID [12156]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 78.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _exact, _rational, _Bernoulli]
\[ \boxed {\frac {3 y^{2}}{x^{4}}-\frac {2 y y^{\prime }}{x^{3}}=-\frac {1}{x^{2}}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 26
dsolve(1/x^2+ 3*y(x)^2/x^4=2*y(x)/x^3*diff(y(x),x),y(x), singsol=all)
\begin{align*} y \left (x \right ) = \sqrt {c_{1} x -1}\, x y \left (x \right ) = -\sqrt {c_{1} x -1}\, x \end{align*}
✓ Solution by Mathematica
Time used: 0.465 (sec). Leaf size: 34
DSolve[1/x^2+ 3*y[x]^2/x^4==2*y[x]/x^3*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x \sqrt {-1+c_1 x} y(x)\to x \sqrt {-1+c_1 x} \end{align*}