38.2.9 problem 9

Internal problem ID [6438]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 24. First order differential equations. Further problems 24. page 1068
Problem number : 9
Date solved : Sunday, March 30, 2025 at 10:58:50 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.038 (sec). Leaf size: 47

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

\[ y = \frac {\operatorname {RootOf}\left (\textit {\_Z}^{8} x^{2} c_1^{2}+4 \textit {\_Z}^{5} x^{2} c_1^{2}-\left (\frac {1}{x c_1}\right )^{{2}/{3}}\right )^{3} x}{2}+\frac {x}{2} \]

✓ Mathematica. Time used: 5.63 (sec). Leaf size: 673

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

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

✓ Sympy. Time used: 0.768 (sec). Leaf size: 29

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

\[ \log {\left (y{\left (x \right )} \right )} = C_{1} - \log {\left (\left (\frac {x}{y{\left (x \right )}} - 2\right )^{\frac {5}{8}} \left (\frac {x}{y{\left (x \right )}} + \frac {2}{3}\right )^{\frac {3}{8}} \right )} \]