28.1.128 problem 151

Internal problem ID [4434]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 151
Date solved : Sunday, March 30, 2025 at 03:22:09 AM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

✓ Maple. Time used: 0.032 (sec). Leaf size: 53

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

\begin{align*} y &= x -1 \\ y &= \frac {\left (-2 x +2 c_1 \right ) \sqrt {-3 c_1 +3 x}}{9}+c_1 \\ y &= \frac {\left (2 x -2 c_1 \right ) \sqrt {-3 c_1 +3 x}}{9}+c_1 \\ \end{align*}

✗ Mathematica

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

Timed out

✗ Sympy

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

Timed Out