60.1.222 problem 227

Internal problem ID [10236]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 227
Date solved : Sunday, March 30, 2025 at 03:33:18 PM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.121 (sec). Leaf size: 33

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

\[ y = \frac {-\sqrt {4-6859 \left (x -\frac {7}{19}\right )^{2} c_1^{2}}+\left (57 x +95\right ) c_1}{76 c_1} \]

✓ Mathematica. Time used: 0.142 (sec). Leaf size: 71

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

\begin{align*} y(x)\to \frac {1}{4} \left (-i \sqrt {19 x^2-14 x-25-16 c_1}+3 x+5\right ) \\ y(x)\to \frac {1}{4} \left (i \sqrt {19 x^2-14 x-25-16 c_1}+3 x+5\right ) \\ \end{align*}

✓ Sympy. Time used: 2.597 (sec). Leaf size: 51

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

\[ \left [ y{\left (x \right )} = \frac {3 x}{4} - \frac {\sqrt {C_{1} - 6859 x^{2} + 5054 x}}{76} + \frac {5}{4}, \ y{\left (x \right )} = \frac {3 x}{4} + \frac {\sqrt {C_{1} - 6859 x^{2} + 5054 x}}{76} + \frac {5}{4}\right ] \]