Internal problem ID [14401]
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: 65.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {y^{\prime }-\frac {-t^{2}+y^{2}}{t y}=0} \] With initial conditions \begin {align*} [y \left (4\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 34
dsolve([diff(y(t),t)=(y(t)^2-t^2)/(t*y(t)),y(4) = 0],y(t), singsol=all)
\begin{align*} y \left (t \right ) &= \sqrt {-2 \ln \left (t \right )+4 \ln \left (2\right )}\, t \\ y \left (t \right ) &= -\sqrt {-2 \ln \left (t \right )+4 \ln \left (2\right )}\, t \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.21 (sec). Leaf size: 36
DSolve[{y'[t]==(y[t]^2-t^2)/(t*y[t]),{y[4]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -t \sqrt {\log (16)-2 \log (t)} \\ y(t)\to t \sqrt {\log (16)-2 \log (t)} \\ \end{align*}