77.1.62 problem 81 (page 120)

Internal problem ID [17881]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 81 (page 120)
Date solved : Monday, March 31, 2025 at 04:46:07 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} y&=2 y^{\prime } x +y^{2} {y^{\prime }}^{3} \end{align*}

✓ Maple. Time used: 0.307 (sec). Leaf size: 95

ode:=y(x) = 2*x*diff(y(x),x)+y(x)^2*diff(y(x),x)^3; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -\frac {2 \left (-x^{3}\right )^{{1}/{4}} 6^{{1}/{4}}}{3} \\ y &= \frac {2 \left (-x^{3}\right )^{{1}/{4}} 6^{{1}/{4}}}{3} \\ y &= -\frac {2 i \left (-x^{3}\right )^{{1}/{4}} 6^{{1}/{4}}}{3} \\ y &= \frac {2 i \left (-x^{3}\right )^{{1}/{4}} 6^{{1}/{4}}}{3} \\ y &= 0 \\ y &= \sqrt {c_1 \left (c_1^{2}+2 x \right )} \\ y &= -\sqrt {c_1 \left (c_1^{2}+2 x \right )} \\ \end{align*}

✓ Mathematica. Time used: 0.105 (sec). Leaf size: 119

ode=y[x]==2*D[y[x],x]*x+y[x]^2*D[y[x],x]^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\sqrt {2 c_1 x+c_1{}^3} \\ y(x)\to \sqrt {2 c_1 x+c_1{}^3} \\ y(x)\to (-1-i) \left (\frac {2}{3}\right )^{3/4} x^{3/4} \\ y(x)\to (1-i) \left (\frac {2}{3}\right )^{3/4} x^{3/4} \\ y(x)\to (-1+i) \left (\frac {2}{3}\right )^{3/4} x^{3/4} \\ y(x)\to (1+i) \left (\frac {2}{3}\right )^{3/4} x^{3/4} \\ \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x*Derivative(y(x), x) - y(x)**2*Derivative(y(x), x)**3 + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

IndexError : list index out of range