23.4.305 problem 308

Internal problem ID [6607]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 4. THE NONLINEAR EQUATION OF SECOND ORDER, page 380
Problem number : 308
Date solved : Tuesday, September 30, 2025 at 03:50:10 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 21

ode:=f(diff(diff(y(x),x),x))+x*diff(diff(y(x),x),x) = diff(y(x),x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\operatorname {RootOf}\left (-f \left (\textit {\_Z} \right )+c_{1} \right ) x^{2}}{2}+c_{1} x +c_{2} \]

✓ Mathematica. Time used: 0.585 (sec). Leaf size: 22

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

\begin{align*} y(x)&\to x f(c_1)+\frac {c_1 x^2}{2}+c_2 \end{align*}

✗ Sympy

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

NotImplementedError : The given ODE -x*Derivative(y(x), (x, 2)) - f(Derivative(y(x), (x, 2))) + Deri