7.5.60 problem 60

Internal problem ID [164]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 60
Date solved : Saturday, March 29, 2025 at 04:37:40 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {2 y-x +7}{4 x -3 y-18} \end{align*}

✓ Maple. Time used: 0.247 (sec). Leaf size: 56

ode:=diff(y(x),x) = (2*y(x)-x+7)/(4*x-3*y(x)-18); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (-x +3\right ) {\operatorname {RootOf}\left (-4+\left (3 c_1 \,x^{4}-36 c_1 \,x^{3}+162 c_1 \,x^{2}-324 c_1 x +243 c_1 \right ) \textit {\_Z}^{20}-\textit {\_Z}^{4}\right )}^{4}}{3}-\frac {x}{3}-1 \]

✓ Mathematica. Time used: 60.066 (sec). Leaf size: 1511

ode=D[y[x],x]==(2*y[x]-x+7)/(4*x-3*y[x]-18); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Sympy. Time used: 1.197 (sec). Leaf size: 36

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x - 2*y(x) - 7)/(4*x - 3*y(x) - 18) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \log {\left (y{\left (x \right )} + 2 \right )} = C_{1} + \log {\left (\frac {\sqrt [4]{\frac {x - 3}{y{\left (x \right )} + 2} - 1}}{\left (\frac {x - 3}{y{\left (x \right )} + 2} + 3\right )^{\frac {5}{4}}} \right )} \]