60.2.218 problem 794
Internal
problem
ID
[10805]
Book
:
Differential
Gleichungen,
E.
Kamke,
3rd
ed.
Chelsea
Pub.
NY,
1948
Section
:
Chapter
1,
Additional
non-linear
first
order
Problem
number
:
794
Date
solved
:
Tuesday, January 28, 2025 at 05:16:25 PM
CAS
classification
:
[_rational]
\begin{align*} y^{\prime }&=\frac {y}{x \left (-1+y+x^{2} y^{3}+y^{4} x^{3}\right )} \end{align*}
✓ Solution by Maple
Time used: 0.030 (sec). Leaf size: 205
dsolve(diff(y(x),x) = y(x)/x/(-1+y(x)+x^2*y(x)^3+y(x)^4*x^3),y(x), singsol=all)
\begin{align*}
y &= 0 \\
y &= \frac {-\left (116+12 \sqrt {93}\right )^{{2}/{3}}-4-2 \left (116+12 \sqrt {93}\right )^{{1}/{3}}}{6 \left (116+12 \sqrt {93}\right )^{{1}/{3}} x} \\
y &= \frac {i \sqrt {3}\, \left (116+12 \sqrt {3}\, \sqrt {31}\right )^{{2}/{3}}-4 i \sqrt {3}+\left (116+12 \sqrt {3}\, \sqrt {31}\right )^{{2}/{3}}-4 \left (116+12 \sqrt {3}\, \sqrt {31}\right )^{{1}/{3}}+4}{12 \left (116+12 \sqrt {3}\, \sqrt {31}\right )^{{1}/{3}} x} \\
y &= \frac {-i \left (116+12 \sqrt {93}\right )^{{2}/{3}} \sqrt {3}+4 i \sqrt {3}+\left (116+12 \sqrt {93}\right )^{{2}/{3}}-4 \left (116+12 \sqrt {93}\right )^{{1}/{3}}+4}{12 \left (116+12 \sqrt {93}\right )^{{1}/{3}} x} \\
-y+\int _{}^{x y}\frac {1}{\textit {\_a} \left (\textit {\_a}^{3}+\textit {\_a}^{2}+1\right )}d \textit {\_a} -c_{1} &= 0 \\
\end{align*}
✓ Solution by Mathematica
Time used: 0.260 (sec). Leaf size: 395
DSolve[D[y[x],x] == y[x]/(x*(-1 + y[x] + x^2*y[x]^3 + x^3*y[x]^4)),y[x],x,IncludeSingularSolutions -> True]
\[
\text {Solve}\left [\int _1^{y(x)}\left (\exp \left (\int _1^{x K[3]}-\frac {(4 K[1]+3) K[1]^2+1}{K[1]^4+K[1]^3+K[1]}dK[1]\right ) x^4 K[3]^4+\exp \left (\int _1^{x K[3]}-\frac {(4 K[1]+3) K[1]^2+1}{K[1]^4+K[1]^3+K[1]}dK[1]\right ) x^3 K[3]^3+\exp \left (\int _1^{x K[3]}-\frac {(4 K[1]+3) K[1]^2+1}{K[1]^4+K[1]^3+K[1]}dK[1]\right ) x K[3]-\exp \left (\int _1^{x K[3]}-\frac {(4 K[1]+3) K[1]^2+1}{K[1]^4+K[1]^3+K[1]}dK[1]\right ) x-\int _1^x\left (\frac {\exp \left (\int _1^{K[2] K[3]}-\frac {(4 K[1]+3) K[1]^2+1}{K[1]^4+K[1]^3+K[1]}dK[1]\right ) K[2] K[3] \left (K[2]^2 (4 K[2] K[3]+3) K[3]^2+1\right )}{K[2]^4 K[3]^4+K[2]^3 K[3]^3+K[2] K[3]}-\exp \left (\int _1^{K[2] K[3]}-\frac {(4 K[1]+3) K[1]^2+1}{K[1]^4+K[1]^3+K[1]}dK[1]\right )\right )dK[2]\right )dK[3]+\int _1^x-\exp \left (\int _1^{K[2] y(x)}-\frac {(4 K[1]+3) K[1]^2+1}{K[1]^4+K[1]^3+K[1]}dK[1]\right ) y(x)dK[2]=c_1,y(x)\right ]
\]