Internal problem ID [13456]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 8. Review exercises for part of part II. page 143
Problem number: 34.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Bernoulli]
\[ \boxed {y^{\prime }-4 y+\frac {16 \,{\mathrm e}^{4 x}}{y^{2}}=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 75
dsolve(diff(y(x),x)=4*y(x)-16*exp(4*x)/y(x)^2,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \left ({\mathrm e}^{4 x} \left ({\mathrm e}^{8 x} c_{1} +6\right )\right )^{\frac {1}{3}} \\ y \left (x \right ) &= -\frac {\left ({\mathrm e}^{4 x} \left ({\mathrm e}^{8 x} c_{1} +6\right )\right )^{\frac {1}{3}} \left (1+i \sqrt {3}\right )}{2} \\ y \left (x \right ) &= \frac {\left ({\mathrm e}^{4 x} \left ({\mathrm e}^{8 x} c_{1} +6\right )\right )^{\frac {1}{3}} \left (i \sqrt {3}-1\right )}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 3.622 (sec). Leaf size: 90
DSolve[y'[x]==4*y[x]-16*Exp[4*x]/y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{4 x/3} \sqrt [3]{6+c_1 e^{8 x}} \\ y(x)\to -\sqrt [3]{-1} e^{4 x/3} \sqrt [3]{6+c_1 e^{8 x}} \\ y(x)\to (-1)^{2/3} e^{4 x/3} \sqrt [3]{6+c_1 e^{8 x}} \\ \end{align*}