6.5.15 problem 11

Internal problem ID [1639]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable Equations. Section 2.4 Page 68
Problem number : 11
Date solved : Tuesday, September 30, 2025 at 04:41:02 AM
CAS classification : [_rational, _Bernoulli]

\begin{align*} y^{\prime }-4 y&=\frac {48 x}{y^{2}} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.102 (sec). Leaf size: 17

ode:=diff(y(x),x)-4*y(x) = 48*x/y(x)^2; 
ic:=[y(0) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \left (2 \,{\mathrm e}^{12 x}-12 x -1\right )^{{1}/{3}} \]

✓ Mathematica. Time used: 3.894 (sec). Leaf size: 21

ode=D[y[x],x]-4*y[x]==48*x/y[x]^2; 
ic=y[0]==1; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \sqrt [3]{-12 x+2 e^{12 x}-1} \end{align*}

✓ Sympy. Time used: 35.035 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-48*x/y(x)**2 - 4*y(x) + Derivative(y(x), x),0) 
ics = {y(0): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \sqrt [3]{- 12 x + 2 e^{12 x} - 1} \]