Internal problem ID [14443]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Review exercises, page 80
Problem number: 40 (b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\frac {t}{y^{3}}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 46
dsolve([diff(y(t),t)=t/y(t)^3,y(0) = 0],y(t), singsol=all)
\begin{align*} y \left (t \right ) &= 2^{\frac {1}{4}} \sqrt {t} \\ y \left (t \right ) &= -2^{\frac {1}{4}} \sqrt {t} \\ y \left (t \right ) &= -i 2^{\frac {1}{4}} \sqrt {t} \\ y \left (t \right ) &= i 2^{\frac {1}{4}} \sqrt {t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.187 (sec). Leaf size: 76
DSolve[{y'[t]==t/y[t]^3,{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\sqrt [4]{2} \sqrt [4]{t^2} \\ y(t)\to -i \sqrt [4]{2} \sqrt [4]{t^2} \\ y(t)\to i \sqrt [4]{2} \sqrt [4]{t^2} \\ y(t)\to \sqrt [4]{2} \sqrt [4]{t^2} \\ \end{align*}