17.1.7 problem 1.1-2 (g)

Internal problem ID [3424]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.1-2, page 6
Problem number : 1.1-2 (g)
Date solved : Monday, January 27, 2025 at 07:36:16 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\frac {t}{\sqrt {t}+1} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 27

dsolve(diff(y(t),t)=t/(sqrt(t)+1),y(t), singsol=all)
 

\[ y = \frac {2 t^{{3}/{2}}}{3}-t +2 \sqrt {t}-2 \ln \left (\sqrt {t}+1\right )+c_{1} \]

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 25

DSolve[D[y[t],t]==1/(1+Sqrt[t]),y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 2 \sqrt {t}-2 \log \left (\sqrt {t}+1\right )+c_1 \]