29.17.13 problem 472
Internal
problem
ID
[5070]
Book
:
Ordinary
differential
equations
and
their
solutions.
By
George
Moseley
Murphy.
1960
Section
:
Various
17
Problem
number
:
472
Date
solved
:
Sunday, March 30, 2025 at 06:34:54 AM
CAS
classification
:
[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\begin{align*} \left (19+9 x +2 y\right ) y^{\prime }+18-2 x -6 y&=0 \end{align*}
✓ Maple. Time used: 1.723 (sec). Leaf size: 31
ode:=(19+9*x+2*y(x))*diff(y(x),x)+18-2*x-6*y(x) = 0;
dsolve(ode,y(x), singsol=all);
\[
y = \frac {-\sqrt {1+\left (-40 x -120\right ) c_1}-1+\left (4 x +44\right ) c_1}{8 c_1}
\]
✓ Mathematica. Time used: 14.727 (sec). Leaf size: 276
ode=(19+9 x+2 y[x])D[y[x],x]+18-2 x-6 y[x]==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*}
y(x)\to -\frac {9 x}{2}+\frac {(5-5 i) (x+3)}{\frac {i \sqrt {2}}{\sqrt {(x+3) \cosh \left (\frac {2 c_1}{9}\right )+(x+3) \sinh \left (\frac {2 c_1}{9}\right )-i}}+(1-i)}-\frac {19}{2} \\
y(x)\to -\frac {9 x}{2}+\frac {(5-5 i) (x+3)}{(1-i)-\frac {i \sqrt {2}}{\sqrt {(x+3) \cosh \left (\frac {2 c_1}{9}\right )+(x+3) \sinh \left (\frac {2 c_1}{9}\right )-i}}}-\frac {19}{2} \\
y(x)\to -\frac {9 x}{2}+\frac {(5-5 i) (x+3)}{(1-i)-\frac {\sqrt {2}}{\sqrt {(x+3) \cosh \left (\frac {2 c_1}{9}\right )+(x+3) \sinh \left (\frac {2 c_1}{9}\right )+i}}}-\frac {19}{2} \\
y(x)\to -\frac {9 x}{2}+\frac {(5-5 i) (x+3)}{\frac {\sqrt {2}}{\sqrt {(x+3) \cosh \left (\frac {2 c_1}{9}\right )+(x+3) \sinh \left (\frac {2 c_1}{9}\right )+i}}+(1-i)}-\frac {19}{2} \\
y(x)\to -2 (x+1) \\
y(x)\to \frac {x+11}{2} \\
\end{align*}
✓ Sympy. Time used: 2.538 (sec). Leaf size: 51
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(-2*x + (9*x + 2*y(x) + 19)*Derivative(y(x), x) - 6*y(x) + 18,0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\left [ y{\left (x \right )} = \frac {C_{1}}{2} + \frac {x}{2} - \frac {\sqrt {C_{1} \left (C_{1} + 10 x + 30\right )}}{2} + \frac {11}{2}, \ y{\left (x \right )} = \frac {C_{1}}{2} + \frac {x}{2} + \frac {\sqrt {C_{1} \left (C_{1} + 10 x + 30\right )}}{2} + \frac {11}{2}\right ]
\]