Internal problem ID [12471]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 73.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type
[_exact, _rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]
\[ \boxed {y-\left (4 y-x \right ) y^{\prime }=3 x^{2}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 47
dsolve((y(x)-3*x^2)-(4*y(x)-x)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {x}{4}-\frac {\sqrt {-8 x^{3}+x^{2}+8 c_{1}}}{4} \\ y \left (x \right ) &= \frac {x}{4}+\frac {\sqrt {-8 x^{3}+x^{2}+8 c_{1}}}{4} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.229 (sec). Leaf size: 67
DSolve[(y[x]-3*x^2)-(4*y[x]-x)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} \left (x-i \sqrt {8 x^3-x^2-16 c_1}\right ) \\ y(x)\to \frac {1}{4} \left (x+i \sqrt {8 x^3-x^2-16 c_1}\right ) \\ \end{align*}