Internal problem ID [6368]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 77.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {x^{\prime }-4 A k \left (\frac {x}{A}\right )^{\frac {3}{4}}+3 k x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 92
dsolve(diff(x(t),t)=4*A*k*(x(t)/A)^(3/4)-3*k*x(t),x(t), singsol=all)
\[ t +\frac {\ln \left (256 A -81 x \relax (t )\right )}{3 k}-\frac {\ln \left (9 \sqrt {\frac {x \relax (t )}{A}}+16\right )}{3 k}+\frac {\ln \left (9 \sqrt {\frac {x \relax (t )}{A}}-16\right )}{3 k}+\frac {2 \ln \left (3 \left (\frac {x \relax (t )}{A}\right )^{\frac {1}{4}}-4\right )}{3 k}-\frac {2 \ln \left (3 \left (\frac {x \relax (t )}{A}\right )^{\frac {1}{4}}+4\right )}{3 k}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.355 (sec). Leaf size: 51
DSolve[x'[t]==4*A*k*(x[t]/A)^(3/4)-3*k*x[t],x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{81} A e^{-3 k t} \left (4 e^{\frac {3 k t}{4}}+e^{\frac {3 c_1}{4}}\right ){}^4 \\ x(t)\to 0 \\ x(t)\to \frac {256 A}{81} \\ \end{align*}