18.1.23 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, March 04, 2025 at 04:41:45 PM
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: 0.712 (sec). Leaf size: 210

ode:=(5*x+y(x)-7)*diff(y(x),x) = 3*x+3*y(x)+3; 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = \frac {\left (x -5\right ) \left (216 \sqrt {\left (x -2\right )^{2} c_{1} \left (-\frac {1}{108}+\left (x -2\right )^{2} c_{1} \right )}+1-216 \left (x -2\right )^{2} c_{1} \right )^{{2}/{3}} \left (\sqrt {3}+i\right )-2 i \left (-11 x +19\right ) \left (216 \sqrt {\left (x -2\right )^{2} c_{1} \left (-\frac {1}{108}+\left (x -2\right )^{2} c_{1} \right )}+1-216 \left (x -2\right )^{2} c_{1} \right )^{{1}/{3}}+\left (x -5\right ) \left (i-\sqrt {3}\right )}{\sqrt {3}\, \left (216 \sqrt {\left (x -2\right )^{2} c_{1} \left (-\frac {1}{108}+\left (x -2\right )^{2} c_{1} \right )}+1-216 \left (x -2\right )^{2} c_{1} \right )^{{2}/{3}}-\sqrt {3}+i \left (216 \sqrt {\left (x -2\right )^{2} c_{1} \left (-\frac {1}{108}+\left (x -2\right )^{2} c_{1} \right )}+1-216 \left (x -2\right )^{2} c_{1} \right )^{{2}/{3}}-2 i \left (216 \sqrt {\left (x -2\right )^{2} c_{1} \left (-\frac {1}{108}+\left (x -2\right )^{2} c_{1} \right )}+1-216 \left (x -2\right )^{2} c_{1} \right )^{{1}/{3}}+i} \]

✓ Mathematica. Time used: 60.184 (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]
 

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✓ Sympy. Time used: 108.827 (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)
 

\[ \left [ y{\left (x \right )} = \frac {\frac {2 i C_{1}}{3 \sqrt [3]{C_{1} \left (18 x + \sqrt {C_{1} + 324 x^{2} - 1296 x + 1296} - 36\right )}} + \sqrt {3} x - i x + \frac {\sqrt {3} \sqrt [3]{C_{1} \left (18 x + \sqrt {C_{1} + 324 x^{2} - 1296 x + 1296} - 36\right )}}{3} + \frac {i \sqrt [3]{C_{1} \left (18 x + \sqrt {C_{1} + 324 x^{2} - 1296 x + 1296} - 36\right )}}{3} - 5 \sqrt {3} + 5 i}{\sqrt {3} - i}, \ y{\left (x \right )} = \frac {- \frac {2 i C_{1}}{3 \sqrt [3]{C_{1} \left (18 x + \sqrt {C_{1} + 324 x^{2} - 1296 x + 1296} - 36\right )}} + \sqrt {3} x + i x + \frac {\sqrt {3} \sqrt [3]{C_{1} \left (18 x + \sqrt {C_{1} + 324 x^{2} - 1296 x + 1296} - 36\right )}}{3} - \frac {i \sqrt [3]{C_{1} \left (18 x + \sqrt {C_{1} + 324 x^{2} - 1296 x + 1296} - 36\right )}}{3} - 5 \sqrt {3} - 5 i}{\sqrt {3} + i}, \ y{\left (x \right )} = \frac {C_{1}}{3 \sqrt [3]{C_{1} \left (18 x + \sqrt {C_{1} + 324 x^{2} - 1296 x + 1296} - 36\right )}} + x - \frac {\sqrt [3]{C_{1} \left (18 x + \sqrt {C_{1} + 324 x^{2} - 1296 x + 1296} - 36\right )}}{3} - 5\right ] \]