44.2.47 problem 49

Internal problem ID [6979]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Section 1.2 Initial value problems. Exercises 1.2 at page 19
Problem number : 49
Date solved : Sunday, March 30, 2025 at 11:32:44 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

\begin{align*} 2 y^{\prime \prime }-3 y^{2}&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Maple. Time used: 0.148 (sec). Leaf size: 40

ode:=2*diff(diff(y(x),x),x)-3*y(x)^2 = 0; 
ic:=y(0) = 0, D(y)(0) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = 4 \operatorname {WeierstrassP}\left (x +\operatorname {RootOf}\left (\operatorname {WeierstrassP}\left (\textit {\_Z} , 0, \operatorname {RootOf}\left (4 \operatorname {WeierstrassPPrime}\left (\operatorname {RootOf}\left (\operatorname {WeierstrassP}\left (\textit {\_Z} , 0, c_2\right )\right ), 0, \textit {\_Z}\right )-1\right )\right )\right ), 0, \operatorname {RootOf}\left (4 \operatorname {WeierstrassPPrime}\left (\operatorname {RootOf}\left (\operatorname {WeierstrassP}\left (\textit {\_Z} , 0, c_2\right )\right ), 0, \textit {\_Z}\right )-1\right )\right ) \]

✗ Mathematica

ode=2*D[y[x],{x,2}]-3*y[x]^2==0; 
ic={y[0] == 0,Derivative[1][y][0] == 1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

{}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*y(x)**2 + 2*Derivative(y(x), (x, 2)),0) 
ics = {y(0): 0, Subs(Derivative(y(x), x), x, 0): 1} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out