60.3.27 problem 1029

Internal problem ID [11023]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1029
Date solved : Thursday, March 13, 2025 at 08:23:34 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-\left (f \left (x \right )^{2}+f^{\prime }\left (x \right )\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.112 (sec). Leaf size: 22

ode:=diff(diff(y(x),x),x)-(f(x)^2+diff(f(x),x))*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (\int {\mathrm e}^{-2 \left (\int fd x \right )}d x +c_{1} \right ) {\mathrm e}^{\int fd x} c_{2} \]

✓ Mathematica. Time used: 0.048 (sec). Leaf size: 58

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

\[ y(x)\to c_1 \exp \left (\int _1^xf(K[1])dK[1]\right )+c_2 \exp \left (\int _1^xf(K[2])dK[2]\right ) \int _1^x\exp \left (\int _1^{K[4]}-2 f(K[3])dK[3]\right )dK[4] \]

✗ Sympy

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

TypeError : cannot determine truth value of Relational