54.1.223 problem 228

Internal problem ID [11537]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 228
Date solved : Tuesday, September 30, 2025 at 08:57:46 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (4 y+11 x -11\right ) y^{\prime }-25 y-8 x +62&=0 \end{align*}

✓ Maple. Time used: 0.231 (sec). Leaf size: 119

ode:=(4*y(x)+11*x-11)*diff(y(x),x)-25*y(x)-8*x+62 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\frac {2}{9}+\frac {\left (1-i \sqrt {3}\right ) \left (12 \sqrt {3}\, \sqrt {-32+177147 \left (x -\frac {1}{9}\right )^{2} c_1^{2}}+\left (-8748 x +972\right ) c_1 \right )^{{2}/{3}}}{108}+\frac {2 i \sqrt {3}}{9}+2 \left (12 \sqrt {3}\, \sqrt {-32+177147 \left (x -\frac {1}{9}\right )^{2} c_1^{2}}-8748 c_1 x +972 c_1 \right )^{{1}/{3}} \left (2 x +1\right ) c_1}{\left (12 \sqrt {3}\, \sqrt {-32+177147 \left (x -\frac {1}{9}\right )^{2} c_1^{2}}+\left (-8748 x +972\right ) c_1 \right )^{{1}/{3}} c_1} \]

✓ Mathematica. Time used: 60.12 (sec). Leaf size: 1677

ode=(4*y[x]+11*x-11)*D[y[x],x]-25*y[x]-8*x+62==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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✓ Sympy. Time used: 129.979 (sec). Leaf size: 410

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-8*x + (11*x + 4*y(x) - 11)*Derivative(y(x), x) - 25*y(x) + 62,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = \frac {- \frac {2 \cdot 6^{\frac {2}{3}} i C_{1}}{3 \sqrt [3]{C_{1} \left (- 81 x + \sqrt {3} \sqrt {- 16 C_{1} + 2187 x^{2} - 486 x + 27} + 9\right )}} + 4 \sqrt {3} x - 4 i x + \frac {\sqrt [3]{2} \cdot 3^{\frac {5}{6}} \sqrt [3]{C_{1} \left (- 81 x + \sqrt {3} \sqrt {- 16 C_{1} + 2187 x^{2} - 486 x + 27} + 9\right )}}{6} + \frac {\sqrt [3]{6} i \sqrt [3]{C_{1} \left (- 81 x + \sqrt {3} \sqrt {- 16 C_{1} + 2187 x^{2} - 486 x + 27} + 9\right )}}{6} + 2 \sqrt {3} - 2 i}{\sqrt {3} - i}, \ y{\left (x \right )} = \frac {\frac {2 \cdot 6^{\frac {2}{3}} i C_{1}}{3 \sqrt [3]{C_{1} \left (- 81 x + \sqrt {3} \sqrt {- 16 C_{1} + 2187 x^{2} - 486 x + 27} + 9\right )}} + 4 \sqrt {3} x + 4 i x + \frac {\sqrt [3]{2} \cdot 3^{\frac {5}{6}} \sqrt [3]{C_{1} \left (- 81 x + \sqrt {3} \sqrt {- 16 C_{1} + 2187 x^{2} - 486 x + 27} + 9\right )}}{6} - \frac {\sqrt [3]{6} i \sqrt [3]{C_{1} \left (- 81 x + \sqrt {3} \sqrt {- 16 C_{1} + 2187 x^{2} - 486 x + 27} + 9\right )}}{6} + 2 \sqrt {3} + 2 i}{\sqrt {3} + i}, \ y{\left (x \right )} = - \frac {6^{\frac {2}{3}} C_{1}}{3 \sqrt [3]{C_{1} \left (- 81 x + \sqrt {3} \sqrt {- 16 C_{1} + 2187 x^{2} - 486 x + 27} + 9\right )}} + 4 x - \frac {\sqrt [3]{6} \sqrt [3]{C_{1} \left (- 81 x + \sqrt {3} \sqrt {- 16 C_{1} + 2187 x^{2} - 486 x + 27} + 9\right )}}{6} + 2\right ] \]