75.3.31 problem 32

Internal problem ID [19935]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter III. Ordinary differential equations of the first order and first degree. Exercises at page 33
Problem number : 32
Date solved : Thursday, October 02, 2025 at 05:03:42 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (x -3 y+4\right ) y^{\prime }&=5 x -7 y \end{align*}

✓ Maple. Time used: 1.542 (sec). Leaf size: 28

ode:=(x-3*y(x)+4)*diff(y(x),x) = 5*x-7*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-1+\sqrt {1+\left (-48 x +168\right ) c_1}+60 \left (-2+x \right ) c_1}{36 c_1} \]

✓ Mathematica. Time used: 60.091 (sec). Leaf size: 1339

ode=(x-3*y[x]+4)*D[y[x],x]==5*x-7*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 1.953 (sec). Leaf size: 68

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-5*x + (x - 3*y(x) + 4)*Derivative(y(x), x) + 7*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = \frac {C_{1}}{2} + \frac {5 x}{3} - \frac {\sqrt {3} \sqrt {C_{1} \left (3 C_{1} + 8 x - 28\right )}}{6} - \frac {10}{3}, \ y{\left (x \right )} = \frac {C_{1}}{2} + \frac {5 x}{3} + \frac {\sqrt {3} \sqrt {C_{1} \left (3 C_{1} + 8 x - 28\right )}}{6} - \frac {10}{3}\right ] \]