4.2.33 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
:
Tuesday, September 30, 2025 at 04:25:05 AM
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: 0.020 (sec). Leaf size: 790
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: 13.278 (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. Time used: 23.577 (sec). Leaf size: 272
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)
\[
\left [ y{\left (x \right )} = \frac {\frac {2 x^{2}}{\sqrt [3]{- 8 C_{1} - x^{3} + 4 \sqrt {C_{1} \left (4 C_{1} + x^{3}\right )}}} - 3 x + 3 \sqrt {3} i x - \sqrt [3]{- 8 C_{1} - x^{3} + 4 \sqrt {C_{1} \left (4 C_{1} + x^{3}\right )}} - \sqrt {3} i \sqrt [3]{- 8 C_{1} - x^{3} + 4 \sqrt {C_{1} \left (4 C_{1} + x^{3}\right )}}}{1 - \sqrt {3} i}, \ y{\left (x \right )} = \frac {\frac {2 x^{2}}{\sqrt [3]{- 8 C_{1} - x^{3} + 4 \sqrt {C_{1} \left (4 C_{1} + x^{3}\right )}}} - 3 x - 3 \sqrt {3} i x - \sqrt [3]{- 8 C_{1} - x^{3} + 4 \sqrt {C_{1} \left (4 C_{1} + x^{3}\right )}} + \sqrt {3} i \sqrt [3]{- 8 C_{1} - x^{3} + 4 \sqrt {C_{1} \left (4 C_{1} + x^{3}\right )}}}{1 + \sqrt {3} i}, \ y{\left (x \right )} = - \frac {x^{2}}{\sqrt [3]{- 8 C_{1} - x^{3} + 4 \sqrt {C_{1} \left (4 C_{1} + x^{3}\right )}}} - 3 x - \sqrt [3]{- 8 C_{1} - x^{3} + 4 \sqrt {C_{1} \left (4 C_{1} + x^{3}\right )}}\right ]
\]