28.1.119 problem 142

Internal problem ID [4425]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 142
Date solved : Tuesday, March 04, 2025 at 06:43:02 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

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

✓ Maple. Time used: 0.014 (sec). Leaf size: 14

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

\[ y \left (x \right ) = {\mathrm e}^{x^{2} \left (c_{1} x -1\right )} \]

✓ Mathematica. Time used: 0.267 (sec). Leaf size: 18

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

\[ y(x)\to e^{x^2 (-1+6 c_1 x)} \]

✓ Sympy. Time used: 0.848 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = e^{- x^{2} \left (- C_{1} x + 1\right )} \]