58.1.45 problem 45
Internal
problem
ID
[9116]
Book
:
Second
order
enumerated
odes
Section
:
section
1
Problem
number
:
45
Date
solved
:
Wednesday, March 05, 2025 at 07:24:20 AM
CAS
classification
:
[[_2nd_order, _missing_x]]
\begin{align*} y {y^{\prime \prime }}^{2}+y^{\prime }&=0 \end{align*}
✓ Maple. Time used: 0.100 (sec). Leaf size: 263
ode:=y(x)*diff(diff(y(x),x),x)^2+diff(y(x),x) = 0;
dsolve(ode,y(x), singsol=all);
\begin{align*}
y &= c_{1} \\
y &= 0 \\
-\int _{}^{y}\frac {\textit {\_a}}{\left (\textit {\_a}^{{3}/{2}} \left (c_{1} -3 \sqrt {\textit {\_a}}\right )\right )^{{2}/{3}}}d \textit {\_a} -x -c_{2} &= 0 \\
-\int _{}^{y}\frac {\textit {\_a}}{\left (\textit {\_a}^{{3}/{2}} \left (c_{1} +3 \sqrt {\textit {\_a}}\right )\right )^{{2}/{3}}}d \textit {\_a} -x -c_{2} &= 0 \\
\frac {-4 \left (\int _{}^{y}\frac {\textit {\_a}}{\left (\textit {\_a}^{{3}/{2}} \left (c_{1} -3 \sqrt {\textit {\_a}}\right )\right )^{{2}/{3}}}d \textit {\_a} \right )+2 i \left (-x -c_{2} \right ) \sqrt {3}+2 x +2 c_{2}}{\left (-i \sqrt {3}-1\right )^{2}} &= 0 \\
\frac {-4 \left (\int _{}^{y}\frac {\textit {\_a}}{\left (\textit {\_a}^{{3}/{2}} \left (c_{1} -3 \sqrt {\textit {\_a}}\right )\right )^{{2}/{3}}}d \textit {\_a} \right )+2 i \left (x +c_{2} \right ) \sqrt {3}+2 x +2 c_{2}}{\left (1-i \sqrt {3}\right )^{2}} &= 0 \\
\frac {-4 \left (\int _{}^{y}\frac {\textit {\_a}}{\left (\textit {\_a}^{{3}/{2}} \left (c_{1} +3 \sqrt {\textit {\_a}}\right )\right )^{{2}/{3}}}d \textit {\_a} \right )+2 i \left (-x -c_{2} \right ) \sqrt {3}+2 x +2 c_{2}}{\left (-i \sqrt {3}-1\right )^{2}} &= 0 \\
\frac {-4 \left (\int _{}^{y}\frac {\textit {\_a}}{\left (\textit {\_a}^{{3}/{2}} \left (c_{1} +3 \sqrt {\textit {\_a}}\right )\right )^{{2}/{3}}}d \textit {\_a} \right )+2 i \left (x +c_{2} \right ) \sqrt {3}+2 x +2 c_{2}}{\left (1-i \sqrt {3}\right )^{2}} &= 0 \\
\end{align*}
✓ Mathematica. Time used: 61.031 (sec). Leaf size: 23861
ode=y[x]*D[y[x],{x,2}]^2+D[y[x],x]==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
Too large to display
✗ Sympy
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(y(x)*Derivative(y(x), (x, 2))**2 + Derivative(y(x), x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
NotImplementedError : solve: Cannot solve y(x)*Derivative(y(x), (x, 2))**2 + Derivative(y(x), x)