Internal problem ID [13079]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Bernoulli]
\[ \boxed {y^{\prime }+3 y-\frac {28 \,{\mathrm e}^{2 x}}{y^{3}}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 78
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 )^{\frac {1}{4}} {\mathrm e}^{-3 x} y = -\left (8 \,{\mathrm e}^{14 x}+c_{1} \right )^{\frac {1}{4}} {\mathrm e}^{-3 x} y = -i \left (8 \,{\mathrm e}^{14 x}+c_{1} \right )^{\frac {1}{4}} {\mathrm e}^{-3 x} y = i \left (8 \,{\mathrm e}^{14 x}+c_{1} \right )^{\frac {1}{4}} {\mathrm e}^{-3 x} \end{align*}
✓ Solution by Mathematica
Time used: 0.741 (sec). Leaf size: 104
DSolve[y'[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*}