60.1.537 problem 550
Internal
problem
ID
[10551]
Book
:
Differential
Gleichungen,
E.
Kamke,
3rd
ed.
Chelsea
Pub.
NY,
1948
Section
:
Chapter
1,
linear
first
order
Problem
number
:
550
Date
solved
:
Sunday, March 30, 2025 at 06:00:03 PM
CAS
classification
:
[[_homogeneous, `class G`]]
\begin{align*} {y^{\prime }}^{r}-a y^{s}-b \,x^{\frac {r s}{r -s}}&=0 \end{align*}
✓ Maple. Time used: 0.071 (sec). Leaf size: 64
ode:=diff(y(x),x)^r-a*y(x)^s-b*x^(r*s/(r-s)) = 0;
dsolve(ode,y(x), singsol=all);
\[
-\int _{\textit {\_b}}^{y}\frac {1}{x \left (r -s \right ) \left (a \,\textit {\_a}^{s}+b \,x^{\frac {r s}{r -s}}\right )^{\frac {1}{r}}-r \textit {\_a}}d \textit {\_a} +\frac {\ln \left (x \right )}{r -s}-c_1 = 0
\]
✓ Mathematica. Time used: 1.445 (sec). Leaf size: 488
ode=-(b*x^((r*s)/(r - s))) - a*y[x]^s + D[y[x],x]^r==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\[
\text {Solve}\left [\int _1^{y(x)}\left (\frac {r}{-r x \left (a K[2]^s+b x^{\frac {r s}{r-s}}\right )^{\frac {1}{r}}+s x \left (a K[2]^s+b x^{\frac {r s}{r-s}}\right )^{\frac {1}{r}}+r K[2]}-\int _1^x\left (\frac {a s K[2]^{s-1} \left (a K[2]^s+b K[1]^{\frac {r s}{r-s}}\right )^{\frac {1}{r}-1}}{r K[1] \left (a K[2]^s+b K[1]^{\frac {r s}{r-s}}\right )^{\frac {1}{r}}-s K[1] \left (a K[2]^s+b K[1]^{\frac {r s}{r-s}}\right )^{\frac {1}{r}}-r K[2]}-\frac {r \left (a K[2]^s+b K[1]^{\frac {r s}{r-s}}\right )^{\frac {1}{r}} \left (-\frac {a s^2 K[1] K[2]^{s-1} \left (a K[2]^s+b K[1]^{\frac {r s}{r-s}}\right )^{\frac {1}{r}-1}}{r}+a s K[1] K[2]^{s-1} \left (a K[2]^s+b K[1]^{\frac {r s}{r-s}}\right )^{\frac {1}{r}-1}-r\right )}{\left (r K[1] \left (a K[2]^s+b K[1]^{\frac {r s}{r-s}}\right )^{\frac {1}{r}}-s K[1] \left (a K[2]^s+b K[1]^{\frac {r s}{r-s}}\right )^{\frac {1}{r}}-r K[2]\right )^2}\right )dK[1]\right )dK[2]+\int _1^x\frac {r \left (a y(x)^s+b K[1]^{\frac {r s}{r-s}}\right )^{\frac {1}{r}}}{r K[1] \left (a y(x)^s+b K[1]^{\frac {r s}{r-s}}\right )^{\frac {1}{r}}-s K[1] \left (a y(x)^s+b K[1]^{\frac {r s}{r-s}}\right )^{\frac {1}{r}}-r y(x)}dK[1]=c_1,y(x)\right ]
\]
✗ Sympy
from sympy import *
x = symbols("x")
a = symbols("a")
b = symbols("b")
r = symbols("r")
s = symbols("s")
y = Function("y")
ode = Eq(-a*y(x)**s - b*x**(r*s/(r - s)) + Derivative(y(x), x)**r,0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
Timed Out