75.14.28 problem 354

Internal problem ID [16871]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 14. Differential equations admitting of depression of their order. Exercises page 107
Problem number : 354
Date solved : Monday, March 31, 2025 at 03:34:12 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

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

With initial conditions

\begin{align*} y \left (-2\right )&=1\\ y^{\prime }\left (-2\right )&=-1 \end{align*}

✓ Maple. Time used: 0.046 (sec). Leaf size: 11

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

\[ y = \frac {4}{\left (x +4\right )^{2}} \]

✓ Mathematica. Time used: 0.043 (sec). Leaf size: 12

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

\[ y(x)\to \frac {4}{(x+4)^2} \]

✗ 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(-2): 1, Subs(Derivative(y(x), x), x, -2): -1} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out