Internal problem ID [14451]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.1, page 141
Problem number: 15.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {3 t^{2} y^{\prime \prime }-5 y^{\prime } t -3 y=0} \] With initial conditions \begin {align*} \left [y \left (1\right ) = 1, y^{\prime }\left (1\right ) = {\frac {17}{3}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve([3*t^2*diff(y(t),t$2)-5*t*diff(y(t),t)-3*y(t)=0,y(1) = 1, D(y)(1) = 17/3],y(t), singsol=all)
\[ y \left (t \right ) = -\frac {4}{5 t^{\frac {1}{3}}}+\frac {9 t^{3}}{5} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 22
DSolve[{3*t^2*y''[t]-5*t*y'[t]-3*y[t]==0,{y[1]==1,y'[1]==17/3}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {9 t^3}{5}-\frac {4}{5 \sqrt [3]{t}} \]