Internal problem ID [14204]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number: 46.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {y^{\prime }-\sqrt {\frac {y}{t}}=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.407 (sec). Leaf size: 94
dsolve([diff(y(t),t)=sqrt(y(t)/t),y(1) = 2],y(t), singsol=all)
\begin{align*} y \left (t \right ) &= \frac {{\left (\left (t^{2}\right )^{\frac {1}{4}} \left (\sqrt {2}-1\right )+t \right )}^{2}}{t} \\ y \left (t \right ) &= \frac {{\left (\left (t^{2}\right )^{\frac {1}{4}} \sqrt {2}+\left (t^{2}\right )^{\frac {1}{4}}-t \right )}^{2}}{t} \\ y \left (t \right ) &= \left (-2-2 \sqrt {2}\right ) \sqrt {t}+t +2 \sqrt {2}+3 \\ y \left (t \right ) &= \left (-2+2 \sqrt {2}\right ) \sqrt {t}+t -2 \sqrt {2}+3 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.208 (sec). Leaf size: 57
DSolve[{y'[t]==Sqrt[y[t]/t],{y[1]==2}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to t-2 \left (1+\sqrt {2}\right ) \sqrt {t}+2 \sqrt {2}+3 \\ y(t)\to t+2 \left (\sqrt {2}-1\right ) \sqrt {t}-2 \sqrt {2}+3 \\ \end{align*}