73.7.34 problem 34

Internal problem ID [15192]
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
Date solved : Tuesday, January 28, 2025 at 07:41:30 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Bernoulli]

\begin{align*} y^{\prime }&=4 y-\frac {16 \,{\mathrm e}^{4 x}}{y^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.049 (sec). Leaf size: 73

dsolve(diff(y(x),x)=4*y(x)-16*exp(4*x)/y(x)^2,y(x), singsol=all)
 

\begin{align*} y &= \left ({\mathrm e}^{4 x} \left ({\mathrm e}^{8 x} c_{1} +6\right )\right )^{{1}/{3}} \\ y &= -\frac {\left ({\mathrm e}^{4 x} \left ({\mathrm e}^{8 x} c_{1} +6\right )\right )^{{1}/{3}} \left (1+i \sqrt {3}\right )}{2} \\ y &= \frac {\left ({\mathrm e}^{4 x} \left ({\mathrm e}^{8 x} c_{1} +6\right )\right )^{{1}/{3}} \left (i \sqrt {3}-1\right )}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 4.187 (sec). Leaf size: 90

DSolve[D[y[x],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*}