72.7.18 problem 18

Internal problem ID [14759]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.9 page 133
Problem number : 18
Date solved : Tuesday, January 28, 2025 at 07:14:02 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=\frac {y}{\sqrt {t^{3}-3}}+t \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 33

dsolve(diff(y(t),t)=y(t)/sqrt(t^3-3)+t,y(t), singsol=all)
 

\[ y = \left (\int t \,{\mathrm e}^{-\int \frac {1}{\sqrt {t^{3}-3}}d t}d t +c_{1} \right ) {\mathrm e}^{\int \frac {1}{\sqrt {t^{3}-3}}d t} \]

✓ Solution by Mathematica

Time used: 0.212 (sec). Leaf size: 110

DSolve[D[y[t],t]==y[t]/Sqrt[t^3-3]+t,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{\frac {t \sqrt {1-\frac {t^3}{3}} \operatorname {Hypergeometric2F1}\left (\frac {1}{3},\frac {1}{2},\frac {4}{3},\frac {t^3}{3}\right )}{\sqrt {t^3-3}}} \left (\int _1^t\exp \left (-\frac {\operatorname {Hypergeometric2F1}\left (\frac {1}{3},\frac {1}{2},\frac {4}{3},\frac {K[1]^3}{3}\right ) K[1] \sqrt {1-\frac {K[1]^3}{3}}}{\sqrt {K[1]^3-3}}\right ) K[1]dK[1]+c_1\right ) \]