Internal problem ID [14709]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.6, page 187
Problem number: 34.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
\[ \boxed {t y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }=\frac {45}{8 t^{\frac {7}{2}}}} \] With initial conditions \begin {align*} [y \left (1\right ) = 0, y^{\prime }\left (1\right ) = 0, y^{\prime \prime }\left (1\right ) = 1, y^{\prime \prime \prime }\left (1\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 24
dsolve([t*diff(y(t),t$4)+2*diff(y(t),t$3)=45/8*1/t^(7/2),y(1) = 0, D(y)(1) = 0, (D@@2)(y)(1) = 1, (D@@3)(y)(1) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {13 t^{2}}{8}+\frac {2}{\sqrt {t}}-\frac {15 t \ln \left (t \right )}{4}+\frac {3 t}{2}-\frac {41}{8} \]
✓ Solution by Mathematica
Time used: 0.098 (sec). Leaf size: 31
DSolve[{t*y''''[t]+2*y'''[t]==45/8*1/t^(7/2),{y[1]==0,y'[1]==0,y''[1]==1,y'''[1]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{8} \left (13 t^2+12 t+\frac {16}{\sqrt {t}}-30 t \log (t)-41\right ) \]