Internal problem ID [7121]
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]
\[ \boxed {x^{\prime }-4 A k \left (\frac {x}{A}\right )^{\frac {3}{4}}+3 k x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 85
dsolve(diff(x(t),t)=4*A*k*(x(t)/A)^(3/4)-3*k*x(t),x(t), singsol=all)
\[ \frac {\ln \left (9 \sqrt {\frac {x \left (t \right )}{A}}-16\right )-\ln \left (9 \sqrt {\frac {x \left (t \right )}{A}}+16\right )+2 \ln \left (3 \left (\frac {x \left (t \right )}{A}\right )^{\frac {1}{4}}-4\right )-2 \ln \left (3 \left (\frac {x \left (t \right )}{A}\right )^{\frac {1}{4}}+4\right )+\ln \left (256 A -81 x \left (t \right )\right )+\left (3 t +3 c_{1} \right ) k}{3 k} = 0 \]
✓ Solution by Mathematica
Time used: 0.409 (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*}