10.2.33 problem 34

Internal problem ID [1161]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 34
Date solved : Saturday, March 29, 2025 at 10:43:07 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.024 (sec). Leaf size: 782

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

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

✓ Mathematica. Time used: 19.101 (sec). Leaf size: 484

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

\begin{align*} y(x)\to \frac {\sqrt [3]{2 x^3+\sqrt {4 e^{3 c_1} x^3+e^{6 c_1}}+e^{3 c_1}}}{\sqrt [3]{2}}+\frac {\sqrt [3]{2} x^2}{\sqrt [3]{2 x^3+\sqrt {4 e^{3 c_1} x^3+e^{6 c_1}}+e^{3 c_1}}}-3 x \\ y(x)\to \frac {i \left (\sqrt {3}+i\right ) \sqrt [3]{2 x^3+\sqrt {4 e^{3 c_1} x^3+e^{6 c_1}}+e^{3 c_1}}}{2 \sqrt [3]{2}}-\frac {\left (1+i \sqrt {3}\right ) x^2}{2^{2/3} \sqrt [3]{2 x^3+\sqrt {4 e^{3 c_1} x^3+e^{6 c_1}}+e^{3 c_1}}}-3 x \\ y(x)\to -\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{2 x^3+\sqrt {4 e^{3 c_1} x^3+e^{6 c_1}}+e^{3 c_1}}}{2 \sqrt [3]{2}}+\frac {i \left (\sqrt {3}+i\right ) x^2}{2^{2/3} \sqrt [3]{2 x^3+\sqrt {4 e^{3 c_1} x^3+e^{6 c_1}}+e^{3 c_1}}}-3 x \\ y(x)\to \sqrt [3]{x^3}+\frac {\left (x^3\right )^{2/3}}{x}-3 x \\ y(x)\to \frac {1}{2} \left (i \left (\sqrt {3}+i\right ) \sqrt [3]{x^3}+\frac {\left (-1-i \sqrt {3}\right ) \left (x^3\right )^{2/3}}{x}-6 x\right ) \\ y(x)\to \frac {1}{2} \left (\left (-1-i \sqrt {3}\right ) \sqrt [3]{x^3}+\frac {i \left (\sqrt {3}+i\right ) \left (x^3\right )^{2/3}}{x}-6 x\right ) \\ \end{align*}

✗ Sympy

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

ZeroDivisionError : polynomial division