69.1.53 problem 72

Internal problem ID [14206]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 72
Date solved : Tuesday, January 28, 2025 at 06:21:54 AM
CAS classification : [_exact, _rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]

\begin{align*} x^{2}+y+\left (x -2 y\right ) y^{\prime }&=0 \end{align*}

Solution by Maple

Time used: 0.003 (sec). Leaf size: 51

dsolve((x^2+y(x))+(x-2*y(x))*diff(y(x),x)=0,y(x), singsol=all)
 
\begin{align*} y &= \frac {x}{2}-\frac {\sqrt {12 x^{3}+9 x^{2}+36 c_{1}}}{6} \\ y &= \frac {x}{2}+\frac {\sqrt {12 x^{3}+9 x^{2}+36 c_{1}}}{6} \\ \end{align*}

Solution by Mathematica

Time used: 0.155 (sec). Leaf size: 81

DSolve[(x^2+y[x])+(x-2*y[x])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 
\begin{align*} y(x)\to \frac {1}{6} \left (3 x-i \sqrt {3} \sqrt {-4 x^3-3 x^2-12 c_1}\right ) \\ y(x)\to \frac {1}{6} \left (3 x+i \sqrt {3} \sqrt {-4 x^3-3 x^2-12 c_1}\right ) \\ \end{align*}