85.69.5 problem 5

Internal problem ID [22921]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. C Exercises at page 217
Problem number : 5
Date solved : Thursday, October 02, 2025 at 09:16:38 PM
CAS classification : [[_2nd_order, _with_exponential_symmetries], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1]]

\begin{align*} y^{\prime \prime }&={y^{\prime }}^{2} \left (2+x y^{\prime }-4 y^{2} y^{\prime }\right ) \end{align*}

✓ Maple. Time used: 0.024 (sec). Leaf size: 33

ode:=diff(diff(y(x),x),x) = diff(y(x),x)^2*(2+x*diff(y(x),x)-4*y(x)^2*diff(y(x),x)); 
dsolve(ode,y(x), singsol=all);
 

\[ \frac {\left (-4 y^{2}+x +16 y-24\right ) {\mathrm e}^{y}+c_1 y-c_2}{y} = 0 \]

✗ Mathematica

ode=D[y[x],{x,2}]==D[y[x],x]^2*(2+x*D[y[x],x]-4*y[x]^2*D[y[x],x]); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-(x*Derivative(y(x), x) - 4*y(x)**2*Derivative(y(x), x) + 2)*Derivative(y(x), x)**2 + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out