Internal problem ID [14353]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.5, page 64
Problem number: 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Bernoulli]
\[ \boxed {y^{\prime }-\frac {y}{t}-t^{2} y^{\frac {3}{2}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(diff(y(t),t)-1/t*y(t)=t^2*y(t)^(3/2),y(t), singsol=all)
\[ \frac {1}{\sqrt {y \left (t \right )}}+\frac {t^{3}}{7}-\frac {c_{1}}{\sqrt {t}} = 0 \]
✓ Solution by Mathematica
Time used: 0.245 (sec). Leaf size: 25
DSolve[y'[t]-1/t*y[t]==t^2*y[t]^(3/2),y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {49 t}{\left (t^{7/2}-7 c_1\right ){}^2} \\ y(t)\to 0 \\ \end{align*}