60.1.381 problem 390
Internal
problem
ID
[10395]
Book
:
Differential
Gleichungen,
E.
Kamke,
3rd
ed.
Chelsea
Pub.
NY,
1948
Section
:
Chapter
1,
linear
first
order
Problem
number
:
390
Date
solved
:
Sunday, March 30, 2025 at 04:36:06 PM
CAS
classification
:
[_dAlembert]
\begin{align*} {y^{\prime }}^{2}+a y y^{\prime }-b x -c&=0 \end{align*}
✓ Maple. Time used: 0.075 (sec). Leaf size: 290
ode:=diff(y(x),x)^2+a*y(x)*diff(y(x),x)-b*x-c = 0;
dsolve(ode,y(x), singsol=all);
\[
y = \frac {{\mathrm e}^{\operatorname {RootOf}\left (\sqrt {a}\, c_1 b \,{\mathrm e}^{2 \textit {\_Z}}-{\mathrm e}^{2 \textit {\_Z}} a b x -{\mathrm e}^{2 \textit {\_Z}} \textit {\_Z} b -{\mathrm e}^{2 \textit {\_Z}} a c +\sqrt {a}\, c_1 \,b^{2}+a \,b^{2} x -\textit {\_Z} \,b^{2}+a b c \right )} \left (-{\mathrm e}^{2 \operatorname {RootOf}\left (\sqrt {a}\, c_1 b \,{\mathrm e}^{2 \textit {\_Z}}-{\mathrm e}^{2 \textit {\_Z}} a b x -{\mathrm e}^{2 \textit {\_Z}} \textit {\_Z} b -{\mathrm e}^{2 \textit {\_Z}} a c +\sqrt {a}\, c_1 \,b^{2}+a \,b^{2} x -\textit {\_Z} \,b^{2}+a b c \right )}-2 b -{\mathrm e}^{-2 \operatorname {RootOf}\left (\sqrt {a}\, c_1 b \,{\mathrm e}^{2 \textit {\_Z}}-{\mathrm e}^{2 \textit {\_Z}} a b x -{\mathrm e}^{2 \textit {\_Z}} \textit {\_Z} b -{\mathrm e}^{2 \textit {\_Z}} a c +\sqrt {a}\, c_1 \,b^{2}+a \,b^{2} x -\textit {\_Z} \,b^{2}+a b c \right )} b^{2}+4 a b x +4 a c \right )}{a^{{3}/{2}} \left (2 \,{\mathrm e}^{2 \operatorname {RootOf}\left (\sqrt {a}\, c_1 b \,{\mathrm e}^{2 \textit {\_Z}}-{\mathrm e}^{2 \textit {\_Z}} a b x -{\mathrm e}^{2 \textit {\_Z}} \textit {\_Z} b -{\mathrm e}^{2 \textit {\_Z}} a c +\sqrt {a}\, c_1 \,b^{2}+a \,b^{2} x -\textit {\_Z} \,b^{2}+a b c \right )}+2 b \right )}
\]
✓ Mathematica. Time used: 0.956 (sec). Leaf size: 193
ode=-c - b*x + a*y[x]*D[y[x],x] + D[y[x],x]^2==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\[
\text {Solve}\left [\left \{x=\exp \left (\int _1^{K[1]}-\frac {b}{a K[2]^2 \left (K[2]-\frac {b}{a K[2]}\right )}dK[2]\right ) \int \frac {\left (-\frac {c-K[1]^2}{a K[1]^2}-\frac {2}{a}\right ) \exp \left (-\int _1^{K[1]}-\frac {b}{a K[2]^2 \left (K[2]-\frac {b}{a K[2]}\right )}dK[2]\right )}{K[1]-\frac {b}{a K[1]}} \, dK[1]+c_1 \exp \left (\int _1^{K[1]}-\frac {b}{a K[2]^2 \left (K[2]-\frac {b}{a K[2]}\right )}dK[2]\right ),y(x)=\frac {b x}{a K[1]}+\frac {c-K[1]^2}{a K[1]}\right \},\{y(x),K[1]\}\right ]
\]
✗ Sympy
from sympy import *
x = symbols("x")
a = symbols("a")
b = symbols("b")
c = symbols("c")
y = Function("y")
ode = Eq(a*y(x)*Derivative(y(x), x) - b*x - c + Derivative(y(x), x)**2,0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
Timed Out