15.6.18 problem 18

Internal problem ID [2975]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 10, page 41
Problem number : 18
Date solved : Sunday, March 30, 2025 at 01:02:57 AM
CAS classification : [_linear]

\begin{align*} y x^{\prime }&=2 y \,{\mathrm e}^{3 y}+x \left (3 y +2\right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

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

\[ x = \left (c_1 y -2\right ) y \,{\mathrm e}^{3 y} \]

✓ Mathematica. Time used: 0.065 (sec). Leaf size: 18

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

\[ x(y)\to e^{3 y} y (-2+c_1 y) \]

✓ Sympy. Time used: 0.316 (sec). Leaf size: 14

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

\[ x{\left (y \right )} = y \left (C_{1} y - 2\right ) e^{3 y} \]