60.1.395 problem 406
Internal
problem
ID
[10409]
Book
:
Differential
Gleichungen,
E.
Kamke,
3rd
ed.
Chelsea
Pub.
NY,
1948
Section
:
Chapter
1,
linear
first
order
Problem
number
:
406
Date
solved
:
Wednesday, March 05, 2025 at 10:46:18 AM
CAS
classification
:
[_dAlembert]
\begin{align*} a {y^{\prime }}^{2}-y y^{\prime }-x&=0 \end{align*}
✓ Maple. Time used: 0.045 (sec). Leaf size: 269
ode:=a*diff(y(x),x)^2-y(x)*diff(y(x),x)-x = 0;
dsolve(ode,y(x), singsol=all);
\begin{align*}
\frac {-\frac {\sqrt {2}\, \left (y+\sqrt {4 a x +y^{2}}\right ) \operatorname {arcsinh}\left (\frac {y+\sqrt {4 a x +y^{2}}}{2 a}\right )}{2}+x \sqrt {\frac {y \sqrt {4 a x +y^{2}}+2 a^{2}+2 a x +y^{2}}{a^{2}}}+c_{1} y+\sqrt {4 a x +y^{2}}\, c_{1}}{\sqrt {\frac {y \sqrt {4 a x +y^{2}}+y^{2}+2 a \left (a +x \right )}{a^{2}}}} &= 0 \\
\frac {\frac {\sqrt {2}\, \left (y-\sqrt {4 a x +y^{2}}\right ) \operatorname {arcsinh}\left (\frac {-y+\sqrt {4 a x +y^{2}}}{2 a}\right )}{2}-\frac {c_{1} \sqrt {2}\, y}{2}+\frac {c_{1} \sqrt {2}\, \sqrt {4 a x +y^{2}}}{2}+x \sqrt {\frac {y^{2}-y \sqrt {4 a x +y^{2}}+2 a^{2}+2 a x}{a^{2}}}}{\sqrt {\frac {-y \sqrt {4 a x +y^{2}}+y^{2}+2 a \left (a +x \right )}{a^{2}}}} &= 0 \\
\end{align*}
✓ Mathematica. Time used: 0.313 (sec). Leaf size: 117
ode=-x - y[x]*D[y[x],x] + a*D[y[x],x]^2==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\[
\text {Solve}\left [\left \{x=a \exp \left (\int _1^{K[1]}\frac {1}{K[2]^2 \left (K[2]+\frac {1}{K[2]}\right )}dK[2]\right ) \int \frac {\exp \left (-\int _1^{K[1]}\frac {1}{K[2]^2 \left (K[2]+\frac {1}{K[2]}\right )}dK[2]\right )}{K[1]+\frac {1}{K[1]}} \, dK[1]+c_1 \exp \left (\int _1^{K[1]}\frac {1}{K[2]^2 \left (K[2]+\frac {1}{K[2]}\right )}dK[2]\right ),y(x)=a K[1]-\frac {x}{K[1]}\right \},\{y(x),K[1]\}\right ]
\]
✗ Sympy
from sympy import *
x = symbols("x")
a = symbols("a")
y = Function("y")
ode = Eq(a*Derivative(y(x), x)**2 - x - y(x)*Derivative(y(x), x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
Timed Out