29.18.15 problem 491
Internal
problem
ID
[5089]
Book
:
Ordinary
differential
equations
and
their
solutions.
By
George
Moseley
Murphy.
1960
Section
:
Various
18
Problem
number
:
491
Date
solved
:
Sunday, March 30, 2025 at 06:36:57 AM
CAS
classification
:
[_rational, [_Abel, `2nd type`, `class A`]]
\begin{align*} \left (x +4 x^{3}+5 y\right ) y^{\prime }+7 x^{3}+3 x^{2} y+4 y&=0 \end{align*}
✓ Maple. Time used: 0.003 (sec). Leaf size: 588
ode:=(x+4*x^3+5*y(x))*diff(y(x),x)+7*x^3+3*x^2*y(x)+4*y(x) = 0;
dsolve(ode,y(x), singsol=all);
\[
y = \frac {16 \left (-x^{15}+5 x^{13}-10 x^{11}+10 x^{9}-5 x^{7}+x^{5}+48 c_1 \right ) {\operatorname {RootOf}\left (\left (-2 x^{15}+10 x^{13}-20 x^{11}+20 x^{9}-10 x^{7}+2 x^{5}+96 c_1 \right ) \textit {\_Z}^{25}+\left (-35 x^{15}+175 x^{13}-350 x^{11}+350 x^{9}-175 x^{7}+35 x^{5}+1680 c_1 \right ) \textit {\_Z}^{20}+11760 c_1 \,\textit {\_Z}^{15}+41160 c_1 \,\textit {\_Z}^{10}+72030 c_1 \,\textit {\_Z}^{5}+50421 c_1 \right )}^{20}+224 \left (-x^{15}+5 x^{13}-10 x^{11}+10 x^{9}-5 x^{7}+x^{5}+48 c_1 \right ) {\operatorname {RootOf}\left (\left (-2 x^{15}+10 x^{13}-20 x^{11}+20 x^{9}-10 x^{7}+2 x^{5}+96 c_1 \right ) \textit {\_Z}^{25}+\left (-35 x^{15}+175 x^{13}-350 x^{11}+350 x^{9}-175 x^{7}+35 x^{5}+1680 c_1 \right ) \textit {\_Z}^{20}+11760 c_1 \,\textit {\_Z}^{15}+41160 c_1 \,\textit {\_Z}^{10}+72030 c_1 \,\textit {\_Z}^{5}+50421 c_1 \right )}^{15}+784 \left (x^{15}-5 x^{13}+10 x^{11}-10 x^{9}+5 x^{7}-x^{5}+72 c_1 \right ) {\operatorname {RootOf}\left (\left (-2 x^{15}+10 x^{13}-20 x^{11}+20 x^{9}-10 x^{7}+2 x^{5}+96 c_1 \right ) \textit {\_Z}^{25}+\left (-35 x^{15}+175 x^{13}-350 x^{11}+350 x^{9}-175 x^{7}+35 x^{5}+1680 c_1 \right ) \textit {\_Z}^{20}+11760 c_1 \,\textit {\_Z}^{15}+41160 c_1 \,\textit {\_Z}^{10}+72030 c_1 \,\textit {\_Z}^{5}+50421 c_1 \right )}^{10}+2744 \left (-x^{15}+5 x^{13}-10 x^{11}+10 x^{9}-5 x^{7}+x^{5}+48 c_1 \right ) {\operatorname {RootOf}\left (\left (-2 x^{15}+10 x^{13}-20 x^{11}+20 x^{9}-10 x^{7}+2 x^{5}+96 c_1 \right ) \textit {\_Z}^{25}+\left (-35 x^{15}+175 x^{13}-350 x^{11}+350 x^{9}-175 x^{7}+35 x^{5}+1680 c_1 \right ) \textit {\_Z}^{20}+11760 c_1 \,\textit {\_Z}^{15}+41160 c_1 \,\textit {\_Z}^{10}+72030 c_1 \,\textit {\_Z}^{5}+50421 c_1 \right )}^{5}-12005 x^{13}+48020 x^{11}-72030 x^{9}+48020 x^{7}-12005 x^{5}+115248 c_1}{12005 x^{4} \left (x -1\right )^{4} \left (x +1\right )^{4}}
\]
✓ Mathematica. Time used: 60.27 (sec). Leaf size: 9701
ode=(x+4 x^3+5 y[x])D[y[x],x]+7 x^3+3 x^2 y[x]+4 y[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(7*x**3 + 3*x**2*y(x) + (4*x**3 + x + 5*y(x))*Derivative(y(x), x) + 4*y(x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
Timed Out