73.5.24 problem 6.7 (L)

Internal problem ID [15135]
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 : Tuesday, January 28, 2025 at 07:36:19 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Bernoulli]

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

✓ Solution by Maple

Time used: 0.046 (sec). Leaf size: 76

dsolve(diff(y(x),x)+3*y(x)=28*exp(2*x)*1/(y(x)^3),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*}

✓ Solution by Mathematica

Time used: 0.801 (sec). Leaf size: 104

DSolve[D[y[x],x]+3*y[x]==28*Exp[2*x]*1/(y[x]^3),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*}