85.8.2 problem 2 (a)

Internal problem ID [22472]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 1. Differential equations in general. C Exercises at page 33
Problem number : 2 (a)
Date solved : Thursday, October 02, 2025 at 08:40:27 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }+{y^{\prime }}^{2} x&=1 \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 27

ode:=diff(diff(y(x),x),x)+x*diff(y(x),x)^2 = 1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \int \frac {\operatorname {AiryAi}\left (x \right ) c_1 +\operatorname {AiryBi}\left (x \right )}{\operatorname {AiryAi}\left (1, x\right ) c_1 +\operatorname {AiryBi}\left (1, x\right )}d x +c_2 \]

✓ Mathematica. Time used: 60.062 (sec). Leaf size: 38

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

\begin{align*} y(x)&\to \int _1^x\frac {\operatorname {AiryBi}(K[1])+\operatorname {AiryAi}(K[1]) c_1}{\operatorname {AiryBiPrime}(K[1])+\operatorname {AiryAiPrime}(K[1]) c_1}dK[1]+c_2 \end{align*}

✗ Sympy

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

ValueError : Rational Solution doesnt exist