67.5.24 problem 6.7 (L)

Internal problem ID [16422]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 6. Simplifying through simplifiction. Additional exercises. page 114
Problem number : 6.7 (L)
Date solved : Thursday, October 02, 2025 at 01:31:20 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Bernoulli]

\begin{align*} y^{\prime }+3 y&=\frac {28 \,{\mathrm e}^{2 x}}{y^{3}} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 76

ode:=diff(y(x),x)+3*y(x) = 28*exp(2*x)/y(x)^3; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \left (8 \,{\mathrm e}^{14 x}+c_1 \right )^{{1}/{4}} {\mathrm e}^{-3 x} \\ y &= -\left (8 \,{\mathrm e}^{14 x}+c_1 \right )^{{1}/{4}} {\mathrm e}^{-3 x} \\ y &= -i \left (8 \,{\mathrm e}^{14 x}+c_1 \right )^{{1}/{4}} {\mathrm e}^{-3 x} \\ y &= i \left (8 \,{\mathrm e}^{14 x}+c_1 \right )^{{1}/{4}} {\mathrm e}^{-3 x} \\ \end{align*}

✓ Mathematica. Time used: 0.652 (sec). Leaf size: 104

ode=D[y[x],x]+3*y[x]==28*Exp[2*x]*1/(y[x]^3); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -e^{-3 x} \sqrt [4]{8 e^{14 x}+c_1}\\ y(x)&\to -i e^{-3 x} \sqrt [4]{8 e^{14 x}+c_1}\\ y(x)&\to i e^{-3 x} \sqrt [4]{8 e^{14 x}+c_1}\\ y(x)&\to e^{-3 x} \sqrt [4]{8 e^{14 x}+c_1} \end{align*}

✓ Sympy. Time used: 0.917 (sec). Leaf size: 82

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*y(x) + Derivative(y(x), x) - 28*exp(2*x)/y(x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - i \sqrt [4]{C_{1} e^{- 12 x} + 8 e^{2 x}}, \ y{\left (x \right )} = i \sqrt [4]{C_{1} e^{- 12 x} + 8 e^{2 x}}, \ y{\left (x \right )} = - \sqrt [4]{C_{1} e^{- 12 x} + 8 e^{2 x}}, \ y{\left (x \right )} = \sqrt [4]{C_{1} e^{- 12 x} + 8 e^{2 x}}\right ] \]