Internal problem ID [13023]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }-\frac {y}{\sqrt {t^{3}-3}}=t} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(diff(y(t),t)=y(t)/sqrt(t^3-3)+t,y(t), singsol=all)
\[ y \left (t \right ) = \left (\int t \,{\mathrm e}^{-\left (\int \frac {1}{\sqrt {t^{3}-3}}d t \right )}d t +c_{1} \right ) {\mathrm e}^{\int \frac {1}{\sqrt {t^{3}-3}}d t} \]
✓ Solution by Mathematica
Time used: 20.591 (sec). Leaf size: 110
DSolve[y'[t]==y[t]/Sqrt[t^3-3]+t,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{\frac {t \sqrt {1-\frac {t^3}{3}} \operatorname {Hypergeometric2F1}\left (\frac {1}{3},\frac {1}{2},\frac {4}{3},\frac {t^3}{3}\right )}{\sqrt {t^3-3}}} \left (\int _1^t\exp \left (-\frac {\operatorname {Hypergeometric2F1}\left (\frac {1}{3},\frac {1}{2},\frac {4}{3},\frac {K[1]^3}{3}\right ) K[1] \sqrt {1-\frac {K[1]^3}{3}}}{\sqrt {K[1]^3-3}}\right ) K[1]dK[1]+c_1\right ) \]