60.1.308 problem 314
Internal
problem
ID
[10322]
Book
:
Differential
Gleichungen,
E.
Kamke,
3rd
ed.
Chelsea
Pub.
NY,
1948
Section
:
Chapter
1,
linear
first
order
Problem
number
:
314
Date
solved
:
Sunday, March 30, 2025 at 04:09:32 PM
CAS
classification
:
[_Bernoulli]
\begin{align*} x y^{3} y^{\prime }+y^{4}-x \sin \left (x \right )&=0 \end{align*}
✓ Maple. Time used: 0.019 (sec). Leaf size: 156
ode:=x*y(x)^3*diff(y(x),x)+y(x)^4-x*sin(x) = 0;
dsolve(ode,y(x), singsol=all);
\begin{align*}
y &= \frac {{\left (4 \left (-x^{4}+12 x^{2}-24\right ) \cos \left (x \right )+16 \left (x^{3}-6 x \right ) \sin \left (x \right )+c_1 \right )}^{{1}/{4}}}{x} \\
y &= -\frac {{\left (4 \left (-x^{4}+12 x^{2}-24\right ) \cos \left (x \right )+16 \left (x^{3}-6 x \right ) \sin \left (x \right )+c_1 \right )}^{{1}/{4}}}{x} \\
y &= -\frac {i {\left (4 \left (-x^{4}+12 x^{2}-24\right ) \cos \left (x \right )+16 \left (x^{3}-6 x \right ) \sin \left (x \right )+c_1 \right )}^{{1}/{4}}}{x} \\
y &= \frac {i {\left (4 \left (-x^{4}+12 x^{2}-24\right ) \cos \left (x \right )+16 \left (x^{3}-6 x \right ) \sin \left (x \right )+c_1 \right )}^{{1}/{4}}}{x} \\
\end{align*}
✓ Mathematica. Time used: 0.329 (sec). Leaf size: 136
ode=-(x*Sin[x]) + y[x]^4 + x*y[x]^3*D[y[x],x]==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*}
y(x)\to -\frac {\sqrt [4]{4 \int _1^xK[1]^4 \sin (K[1])dK[1]+c_1}}{x} \\
y(x)\to -\frac {i \sqrt [4]{4 \int _1^xK[1]^4 \sin (K[1])dK[1]+c_1}}{x} \\
y(x)\to \frac {i \sqrt [4]{4 \int _1^xK[1]^4 \sin (K[1])dK[1]+c_1}}{x} \\
y(x)\to \frac {\sqrt [4]{4 \int _1^xK[1]^4 \sin (K[1])dK[1]+c_1}}{x} \\
\end{align*}
✓ Sympy. Time used: 9.975 (sec). Leaf size: 197
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(x*y(x)**3*Derivative(y(x), x) - x*sin(x) + y(x)**4,0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\left [ y{\left (x \right )} = - i \sqrt [4]{\frac {C_{1}}{x^{4}} - 4 \cos {\left (x \right )} + \frac {16 \sin {\left (x \right )}}{x} + \frac {48 \cos {\left (x \right )}}{x^{2}} - \frac {96 \sin {\left (x \right )}}{x^{3}} - \frac {96 \cos {\left (x \right )}}{x^{4}}}, \ y{\left (x \right )} = i \sqrt [4]{\frac {C_{1}}{x^{4}} - 4 \cos {\left (x \right )} + \frac {16 \sin {\left (x \right )}}{x} + \frac {48 \cos {\left (x \right )}}{x^{2}} - \frac {96 \sin {\left (x \right )}}{x^{3}} - \frac {96 \cos {\left (x \right )}}{x^{4}}}, \ y{\left (x \right )} = - \sqrt [4]{\frac {C_{1}}{x^{4}} - 4 \cos {\left (x \right )} + \frac {16 \sin {\left (x \right )}}{x} + \frac {48 \cos {\left (x \right )}}{x^{2}} - \frac {96 \sin {\left (x \right )}}{x^{3}} - \frac {96 \cos {\left (x \right )}}{x^{4}}}, \ y{\left (x \right )} = \sqrt [4]{\frac {C_{1}}{x^{4}} - 4 \cos {\left (x \right )} + \frac {16 \sin {\left (x \right )}}{x} + \frac {48 \cos {\left (x \right )}}{x^{2}} - \frac {96 \sin {\left (x \right )}}{x^{3}} - \frac {96 \cos {\left (x \right )}}{x^{4}}}\right ]
\]