74.14.34 problem 34

Internal problem ID [16439]
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
Date solved : Tuesday, January 28, 2025 at 09:07:59 AM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} t y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }&=\frac {45}{8 t^{{7}/{2}}} \end{align*}

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: 0.043 (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)
 

\[ y = \frac {13 t^{2}}{8}+\frac {2}{\sqrt {t}}-\frac {15 t \ln \left (t \right )}{4}+\frac {3 t}{2}-\frac {41}{8} \]

✓ Solution by Mathematica

Time used: 0.095 (sec). Leaf size: 31

DSolve[{t*D[y[t],{t,4}]+2*D[ y[t],{t,3}]==45/8*1/t^(7/2),{y[1]==0,Derivative[1][y][1]==0,Derivative[2][y][1]==1,Derivative[3][y][1]==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{8} \left (13 t^2+12 t+\frac {16}{\sqrt {t}}-30 t \log (t)-41\right ) \]