Internal problem ID [6339]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 48.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
Solve \begin {gather*} \boxed {\left (t^{2}+9\right ) y^{\prime \prime }+2 y^{\prime } t=0} \end {gather*} With initial conditions \begin {align*} \left [y \relax (3) = 2 \pi , y^{\prime }\relax (3) = {\frac {2}{3}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.042 (sec). Leaf size: 12
dsolve([(t^2+9)*diff(y(t),t$2)+2*t*diff(y(t),t)=0,y(3) = 2*Pi, D(y)(3) = 2/3],y(t), singsol=all)
\[ y \relax (t ) = \pi +4 \arctan \left (\frac {t}{3}\right ) \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 15
DSolve[{(t^2+9)*y''[t]+2*t*y'[t]==0,{y[3]==2*Pi,y'[3]==2/3}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to 4 \text {ArcTan}\left (\frac {t}{3}\right )+\pi \\ \end{align*}