60.1.466 problem 479
Internal
problem
ID
[10480]
Book
:
Differential
Gleichungen,
E.
Kamke,
3rd
ed.
Chelsea
Pub.
NY,
1948
Section
:
Chapter
1,
linear
first
order
Problem
number
:
479
Date
solved
:
Sunday, March 30, 2025 at 04:51:25 PM
CAS
classification
:
[_rational, _dAlembert]
\begin{align*} \left (b_{2} y+a_{2} x +c_{2} \right ) {y^{\prime }}^{2}+\left (a_{1} x +b_{1} y+c_{1} \right ) y^{\prime }+a_{0} x +b_{0} y+c_{0}&=0 \end{align*}
✓ Maple. Time used: 0.712 (sec). Leaf size: 877
ode:=(b__2*y(x)+a__2*x+c__2)*diff(y(x),x)^2+(a__1*x+b__1*y(x)+c__1)*diff(y(x),x)+a__0*x+b__0*y(x)+c__0 = 0;
dsolve(ode,y(x), singsol=all);
\begin{align*} \text {Solution too large to show}\end{align*}
✓ Mathematica. Time used: 1.886 (sec). Leaf size: 372
ode=c0 + a0*x + b0*y[x] + (c1 + a1*x + b1*y[x])*D[y[x],x] + (c2 + a2*x + b2*y[x])*D[y[x],x]^2==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\[
\text {Solve}\left [\left \{x=-\frac {-(K[3] (\text {b2} K[3]+\text {b1})+\text {b0}) \exp \left (\int _1^{K[3]}\frac {\text {b0}+K[1] (\text {b1}+\text {b2} K[1])}{\text {a0}+K[1] (\text {a1}+\text {b0}+K[1] (\text {a2}+\text {b1}+\text {b2} K[1]))}dK[1]\right ) \left (\int _1^{K[3]}\frac {\exp \left (-\int _1^{K[2]}\frac {\text {b0}+K[1] (\text {b1}+\text {b2} K[1])}{\text {a0}+K[1] (\text {a1}+\text {b0}+K[1] (\text {a2}+\text {b1}+\text {b2} K[1]))}dK[1]\right ) (-\text {c0}-K[2] (\text {c1}+\text {c2} K[2]))}{\text {a0}+K[2] (\text {a1}+\text {b0}+K[2] (\text {a2}+\text {b1}+\text {b2} K[2]))}dK[2]+c_1\right )+\text {c1} K[3]+\text {c2} K[3]^2+\text {c0}}{K[3] (K[3] (\text {b2} K[3]+\text {a2}+\text {b1})+\text {a1}+\text {b0})+\text {a0}},y(x)=-\frac {K[3] (K[3] (\text {c2} K[3]+\text {c1})+\text {c0})+(K[3] (\text {a2} K[3]+\text {a1})+\text {a0}) \exp \left (\int _1^{K[3]}\frac {\text {b0}+K[1] (\text {b1}+\text {b2} K[1])}{\text {a0}+K[1] (\text {a1}+\text {b0}+K[1] (\text {a2}+\text {b1}+\text {b2} K[1]))}dK[1]\right ) \left (\int _1^{K[3]}\frac {\exp \left (-\int _1^{K[2]}\frac {\text {b0}+K[1] (\text {b1}+\text {b2} K[1])}{\text {a0}+K[1] (\text {a1}+\text {b0}+K[1] (\text {a2}+\text {b1}+\text {b2} K[1]))}dK[1]\right ) (-\text {c0}-K[2] (\text {c1}+\text {c2} K[2]))}{\text {a0}+K[2] (\text {a1}+\text {b0}+K[2] (\text {a2}+\text {b1}+\text {b2} K[2]))}dK[2]+c_1\right )}{K[3] (K[3] (\text {b2} K[3]+\text {a2}+\text {b1})+\text {a1}+\text {b0})+\text {a0}}\right \},\{y(x),K[3]\}\right ]
\]
✗ Sympy
from sympy import *
x = symbols("x")
a__0 = symbols("a__0")
a__1 = symbols("a__1")
a__2 = symbols("a__2")
b__0 = symbols("b__0")
b__1 = symbols("b__1")
b__2 = symbols("b__2")
c__0 = symbols("c__0")
c__1 = symbols("c__1")
c__2 = symbols("c__2")
y = Function("y")
ode = Eq(a__0*x + b__0*y(x) + c__0 + (a__1*x + b__1*y(x) + c__1)*Derivative(y(x), x) + (a__2*x + b__2*y(x) + c__2)*Derivative(y(x), x)**2,0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
Timed Out