83.4.6 problem 2 (a)

Internal problem ID [21933]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Chapter III. First order differential equations of the first degree. Ex. V at page 42
Problem number : 2 (a)
Date solved : Thursday, October 02, 2025 at 08:15:39 PM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 4 x -2 y+3+\left (5 y-2 x +7\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.160 (sec). Leaf size: 23

ode:=4*x-2*y(x)+3+(5*y(x)-2*x+7)*diff(y(x),x) = 0; 
ic:=[y(1) = 2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {2 x}{5}-\frac {7}{5}+\frac {\sqrt {-16 x^{2}-58 x +299}}{5} \]

✓ Mathematica. Time used: 0.09 (sec). Leaf size: 32

ode=(4*x-2*y[x]+3 )+(5*y[x]-2*x+7 )*D[y[x],x]==0; 
ic={y[1]==2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{5} \left (-i \sqrt {16 x^2+58 x-299}+2 x-7\right ) \end{align*}

✓ Sympy. Time used: 1.679 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x + (-2*x + 5*y(x) + 7)*Derivative(y(x), x) - 2*y(x) + 3,0) 
ics = {y(1): 2} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {2 x}{5} + \frac {\sqrt {- 256 x^{2} - 928 x + 4784}}{20} - \frac {7}{5} \]