60.1.1 problem 1

Internal problem ID [10015]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 1
Date solved : Wednesday, March 05, 2025 at 08:04:13 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }-\frac {1}{\sqrt {\operatorname {a4} \,x^{4}+\operatorname {a3} \,x^{3}+\operatorname {a2} \,x^{2}+\operatorname {a1} x +\operatorname {a0}}}&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 30

ode:=diff(y(x),x)-1/(a4*x^4+a3*x^3+a2*x^2+a1*x+a0)^(1/2) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \int \frac {1}{\sqrt {\operatorname {a4} \,x^{4}+\operatorname {a3} \,x^{3}+\operatorname {a2} \,x^{2}+\operatorname {a1} x +\operatorname {a0}}}d x +c_{1} \]

✓ Mathematica. Time used: 10.288 (sec). Leaf size: 1117

ode=D[y[x],x] - (a4*x^4+a3*x^3+a2*x^2+a1*x+a0)^(-1/2)==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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✓ Sympy. Time used: 0.564 (sec). Leaf size: 31

from sympy import * 
x = symbols("x") 
a0 = symbols("a0") 
a1 = symbols("a1") 
a2 = symbols("a2") 
a3 = symbols("a3") 
a4 = symbols("a4") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - 1/sqrt(a0 + a1*x + a2*x**2 + a3*x**3 + a4*x**4),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + \int \frac {1}{\sqrt {a_{0} + a_{1} x + a_{2} x^{2} + a_{3} x^{3} + a_{4} x^{4}}}\, dx \]