60.1.69 problem 70

Internal problem ID [10083]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 70
Date solved : Sunday, March 30, 2025 at 03:13:22 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} y^{\prime }-\sqrt {\frac {a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}{b_{4} y^{4}+b_{3} y^{3}+b_{2} y^{2}+b_{1} y+b_{0}}}&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 113

ode:=diff(y(x),x)-((a__4*x^4+a__3*x^3+a__2*x^2+a__1*x+a__0)/(b__4*y(x)^4+b__3*y(x)^3+b__2*y(x)^2+b__1*y(x)+b__0))^(1/2) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \int _{}^{y}\sqrt {\textit {\_a}^{4} b_{4} +\textit {\_a}^{3} b_{3} +\textit {\_a}^{2} b_{2} +\textit {\_a} b_{1} +b_{0}}d \textit {\_a} -\sqrt {b_{4} y^{4}+b_{3} y^{3}+b_{2} y^{2}+b_{1} y+b_{0}}\, \int _{}^{x}\sqrt {\frac {\textit {\_a}^{4} a_{4} +\textit {\_a}^{3} a_{3} +\textit {\_a}^{2} a_{2} +\textit {\_a} a_{1} +a_{0}}{b_{4} y^{4}+b_{3} y^{3}+b_{2} y^{2}+b_{1} y+b_{0}}}d \textit {\_a} +c_1 = 0 \]

✓ Mathematica. Time used: 55.381 (sec). Leaf size: 78

ode=D[y[x],x] - Sqrt[(a4*x^4+a3*x^3+a2*x^2+a1*x+a0)/(b4*y[x]^4+b3*y[x]^3+b2*y[x]^2+b1*y[x]+b0)]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\sqrt {\text {b4} K[1]^4+\text {b3} K[1]^3+\text {b2} K[1]^2+\text {b1} K[1]+\text {b0}}dK[1]\&\right ]\left [\int _1^x\sqrt {\text {a0}+K[2] (\text {a1}+K[2] (\text {a2}+K[2] (\text {a3}+\text {a4} K[2])))}dK[2]+c_1\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
a__0 = symbols("a__0") 
a__1 = symbols("a__1") 
a__2 = symbols("a__2") 
a__3 = symbols("a__3") 
a__4 = symbols("a__4") 
b__0 = symbols("b__0") 
b__1 = symbols("b__1") 
b__2 = symbols("b__2") 
b__3 = symbols("b__3") 
b__4 = symbols("b__4") 
y = Function("y") 
ode = Eq(-sqrt((a__0 + a__1*x + a__2*x**2 + a__3*x**3 + a__4*x**4)/(b__0 + b__1*y(x) + b__2*y(x)**2 + b__3*y(x)**3 + b__4*y(x)**4)) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out