74.7.1 problem 1

Internal problem ID [16078]
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 : 1
Date solved : Tuesday, January 28, 2025 at 08:36:51 AM
CAS classification : [_rational, _Bernoulli]

\begin{align*} y^{\prime }-\frac {y}{2}&=\frac {t}{y} \end{align*}

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 31

dsolve(diff(y(t),t)-1/2*y(t)=t/y(t),y(t), singsol=all)
 

\begin{align*} y &= \sqrt {c_{1} {\mathrm e}^{t}-2 t -2} \\ y &= -\sqrt {c_{1} {\mathrm e}^{t}-2 t -2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.219 (sec). Leaf size: 76

DSolve[D[y[t],t]-1/2*y[t]==t/y[t],y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to -e^{t/2} \sqrt {2 \int _1^te^{-K[1]} K[1]dK[1]+c_1} \\ y(t)\to e^{t/2} \sqrt {2 \int _1^te^{-K[1]} K[1]dK[1]+c_1} \\ \end{align*}