Internal problem ID [12353]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A.
Dobrushkin. CRC Press 2015
Section: Chapter 6. Introduction to Systems of ODEs. Problems page 408
Problem number: Problem 1(c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+3 y^{\prime }+\frac {y}{t}=t} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 36
dsolve(diff(y(t),t$2)+3*diff(y(t),t)+y(t)/t=t,y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (7 \,{\mathrm e}^{-3 t} \operatorname {KummerU}\left (\frac {2}{3}, 2, 3 t \right ) c_{1} +7 \,{\mathrm e}^{-3 t} \operatorname {KummerM}\left (\frac {2}{3}, 2, 3 t \right ) c_{2} +t -\frac {1}{2}\right ) t}{7} \]
✓ Solution by Mathematica
Time used: 23.552 (sec). Leaf size: 253
DSolve[y''[t]+3*y'[t]+y[t]/t==t,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to G_{1,2}^{2,0}\left (3 t\left | \begin {array}{c} \frac {2}{3} \\ 0,1 \\ \end {array} \right .\right ) \left (\int _1^t-\frac {3 \operatorname {Hypergeometric1F1}\left (\frac {4}{3},2,-3 K[2]\right ) K[2]^2}{3 \operatorname {Hypergeometric1F1}\left (\frac {4}{3},2,-3 K[2]\right ) G_{1,2}^{2,0}\left (3 K[2]\left | \begin {array}{c} \frac {2}{3} \\ 0,1 \\ \end {array} \right .\right )+3 \operatorname {Hypergeometric1F1}\left (\frac {4}{3},2,-3 K[2]\right ) G_{1,2}^{2,0}\left (3 K[2]\left | \begin {array}{c} \frac {2}{3} \\ 1,1 \\ \end {array} \right .\right )-2 \operatorname {Hypergeometric1F1}\left (\frac {7}{3},3,-3 K[2]\right ) G_{1,2}^{2,0}\left (3 K[2]\left | \begin {array}{c} \frac {5}{3} \\ 1,2 \\ \end {array} \right .\right )}dK[2]+c_2\right )-3 t \operatorname {Hypergeometric1F1}\left (\frac {4}{3},2,-3 t\right ) \left (\int _1^t\frac {G_{1,2}^{2,0}\left (3 K[1]\left | \begin {array}{c} \frac {5}{3} \\ 1,2 \\ \end {array} \right .\right )}{-9 \operatorname {Hypergeometric1F1}\left (\frac {4}{3},2,-3 K[1]\right ) G_{1,2}^{2,0}\left (3 K[1]\left | \begin {array}{c} \frac {2}{3} \\ 0,1 \\ \end {array} \right .\right )-9 \operatorname {Hypergeometric1F1}\left (\frac {4}{3},2,-3 K[1]\right ) G_{1,2}^{2,0}\left (3 K[1]\left | \begin {array}{c} \frac {2}{3} \\ 1,1 \\ \end {array} \right .\right )+6 \operatorname {Hypergeometric1F1}\left (\frac {7}{3},3,-3 K[1]\right ) G_{1,2}^{2,0}\left (3 K[1]\left | \begin {array}{c} \frac {5}{3} \\ 1,2 \\ \end {array} \right .\right )}dK[1]+c_1\right ) \]