56.1.48 problem 48

Internal problem ID [8760]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 48
Date solved : Monday, January 27, 2025 at 04:48:24 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} \left (t^{2}+9\right ) y^{\prime \prime }+2 t y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (3\right )&=2 \pi \\ y^{\prime }\left (3\right )&={\frac {2}{3}} \end{align*}

✓ Solution by Maple

Time used: 0.048 (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)
 

\[ y = \pi +4 \arctan \left (\frac {t}{3}\right ) \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 15

DSolve[{(t^2+9)*D[y[t],{t,2}]+2*t*D[y[t],t]==0,{y[3]==2*Pi,Derivative[1][y][3 ]==2/3}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 4 \arctan \left (\frac {t}{3}\right )+\pi \]