10.2.32 problem 33
Internal
problem
ID
[1160]
Book
:
Elementary
differential
equations
and
boundary
value
problems,
10th
ed.,
Boyce
and
DiPrima
Section
:
Section
2.2.
Page
48
Problem
number
:
33
Date
solved
:
Saturday, March 29, 2025 at 10:43:02 PM
CAS
classification
:
[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]
\begin{align*} y^{\prime }&=\frac {4 y-3 x}{2 x -y} \end{align*}
✓ Maple. Time used: 0.176 (sec). Leaf size: 26
ode:=diff(y(x),x) = (4*y(x)-3*x)/(2*x-y(x));
dsolve(ode,y(x), singsol=all);
\[
y = x \left (\operatorname {RootOf}\left (x^{4} c_1 \,\textit {\_Z}^{20}-\textit {\_Z}^{4}+4\right )^{4}-3\right )
\]
✓ Mathematica. Time used: 2.989 (sec). Leaf size: 336
ode=D[y[x],x] == (4*y[x]-3*x)/(2*x-y[x]);
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*}
y(x)\to \text {Root}\left [\text {$\#$1}^5+15 \text {$\#$1}^4 x+90 \text {$\#$1}^3 x^2+270 \text {$\#$1}^2 x^3+\text {$\#$1} \left (405 x^4-e^{4 c_1}\right )+243 x^5+e^{4 c_1} x\&,1\right ] \\
y(x)\to \text {Root}\left [\text {$\#$1}^5+15 \text {$\#$1}^4 x+90 \text {$\#$1}^3 x^2+270 \text {$\#$1}^2 x^3+\text {$\#$1} \left (405 x^4-e^{4 c_1}\right )+243 x^5+e^{4 c_1} x\&,2\right ] \\
y(x)\to \text {Root}\left [\text {$\#$1}^5+15 \text {$\#$1}^4 x+90 \text {$\#$1}^3 x^2+270 \text {$\#$1}^2 x^3+\text {$\#$1} \left (405 x^4-e^{4 c_1}\right )+243 x^5+e^{4 c_1} x\&,3\right ] \\
y(x)\to \text {Root}\left [\text {$\#$1}^5+15 \text {$\#$1}^4 x+90 \text {$\#$1}^3 x^2+270 \text {$\#$1}^2 x^3+\text {$\#$1} \left (405 x^4-e^{4 c_1}\right )+243 x^5+e^{4 c_1} x\&,4\right ] \\
y(x)\to \text {Root}\left [\text {$\#$1}^5+15 \text {$\#$1}^4 x+90 \text {$\#$1}^3 x^2+270 \text {$\#$1}^2 x^3+\text {$\#$1} \left (405 x^4-e^{4 c_1}\right )+243 x^5+e^{4 c_1} x\&,5\right ] \\
\end{align*}
✓ Sympy. Time used: 0.966 (sec). Leaf size: 26
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(Derivative(y(x), x) + (3*x - 4*y(x))/(2*x - y(x)),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\log {\left (x \right )} = C_{1} + \log {\left (\frac {\sqrt [4]{-1 + \frac {y{\left (x \right )}}{x}}}{\left (3 + \frac {y{\left (x \right )}}{x}\right )^{\frac {5}{4}}} \right )}
\]