12.1.23 problem Problem 14.28
Internal
problem
ID
[3479]
Book
:
Mathematical
methods
for
physics
and
engineering,
Riley,
Hobson,
Bence,
second
edition,
2002
Section
:
Chapter
14,
First
order
ordinary
differential
equations.
14.4
Exercises,
page
490
Problem
number
:
Problem
14.28
Date
solved
:
Tuesday, September 30, 2025 at 06:39:57 AM
CAS
classification
:
[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\begin{align*} \left (5 x +y-7\right ) y^{\prime }&=3 x +3 y+3 \end{align*}
✓ Maple. Time used: 0.238 (sec). Leaf size: 114
ode:=(5*x+y(x)-7)*diff(y(x),x) = 3*x+3*y(x)+3;
dsolve(ode,y(x), singsol=all);
\[
y = \frac {\frac {1}{2}+\frac {\left (1-i \sqrt {3}\right ) \left (3 \sqrt {3}\, \sqrt {108 \left (x -2\right )^{2} c_1^{2}-1}-54 \left (x -2\right ) c_1 \right )^{{2}/{3}}}{6}+\frac {i \sqrt {3}}{2}+\left (3 \sqrt {3}\, \sqrt {108 \left (x -2\right )^{2} c_1^{2}-1}-54 c_1 x +108 c_1 \right )^{{1}/{3}} \left (x -5\right ) c_1}{\left (3 \sqrt {3}\, \sqrt {108 \left (x -2\right )^{2} c_1^{2}-1}-54 \left (x -2\right ) c_1 \right )^{{1}/{3}} c_1}
\]
✓ Mathematica. Time used: 60.117 (sec). Leaf size: 1626
ode=(5*x+y[x]-7)*D[y[x],x]==3*(x+y[x]+1);
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
Too large to display
✓ Sympy. Time used: 61.561 (sec). Leaf size: 306
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(-3*x + (5*x + y(x) - 7)*Derivative(y(x), x) - 3*y(x) - 3,0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\left [ y{\left (x \right )} = \frac {\frac {2 i C_{1}}{3 \sqrt [3]{C_{1} \left (18 x + \sqrt {C_{1} + 324 x^{2} - 1296 x + 1296} - 36\right )}} + \sqrt {3} x - i x + \frac {\sqrt {3} \sqrt [3]{C_{1} \left (18 x + \sqrt {C_{1} + 324 x^{2} - 1296 x + 1296} - 36\right )}}{3} + \frac {i \sqrt [3]{C_{1} \left (18 x + \sqrt {C_{1} + 324 x^{2} - 1296 x + 1296} - 36\right )}}{3} - 5 \sqrt {3} + 5 i}{\sqrt {3} - i}, \ y{\left (x \right )} = \frac {- \frac {2 i C_{1}}{3 \sqrt [3]{C_{1} \left (18 x + \sqrt {C_{1} + 324 x^{2} - 1296 x + 1296} - 36\right )}} + \sqrt {3} x + i x + \frac {\sqrt {3} \sqrt [3]{C_{1} \left (18 x + \sqrt {C_{1} + 324 x^{2} - 1296 x + 1296} - 36\right )}}{3} - \frac {i \sqrt [3]{C_{1} \left (18 x + \sqrt {C_{1} + 324 x^{2} - 1296 x + 1296} - 36\right )}}{3} - 5 \sqrt {3} - 5 i}{\sqrt {3} + i}, \ y{\left (x \right )} = \frac {C_{1}}{3 \sqrt [3]{C_{1} \left (18 x + \sqrt {C_{1} + 324 x^{2} - 1296 x + 1296} - 36\right )}} + x - \frac {\sqrt [3]{C_{1} \left (18 x + \sqrt {C_{1} + 324 x^{2} - 1296 x + 1296} - 36\right )}}{3} - 5\right ]
\]