85.12.12 problem 12

Internal problem ID [22506]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 40
Problem number : 12
Date solved : Thursday, October 02, 2025 at 08:43:46 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

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

\[ y = x -\frac {1}{2}+\left (3 x -2\right )^{{4}/{3}} c_1 \]

✓ Mathematica. Time used: 0.032 (sec). Leaf size: 27

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

\begin{align*} y(x)&\to \frac {1}{2} \left (2 x+2 c_1 (3 x-2)^{4/3}-1\right ) \end{align*}

✓ Sympy. Time used: 0.239 (sec). Leaf size: 32

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

\[ y{\left (x \right )} = 3 C_{1} x \sqrt [3]{3 x - 2} - 2 C_{1} \sqrt [3]{3 x - 2} + x - \frac {1}{2} \]