76.17.22 problem 31

Internal problem ID [17708]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.7 (Variation of parameters). Problems at page 280
Problem number : 31
Date solved : Tuesday, January 28, 2025 at 11:01:38 AM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} t^{2} y^{\prime \prime }+7 y^{\prime } t +5 y&=t \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 27

dsolve(t^2*diff(y(t),t$2)+7*t*diff(y(t),t)+5*y(t)=t,y(t), singsol=all)
 

\[ y = \frac {t^{6}+3 c_{1} t^{4}-4 c_{1}^{3}+12 c_{2}}{12 t^{5}} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 23

DSolve[t^2*D[y[t],{t,2}]+7*t*D[y[t],t]+5*y[t]==t,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {c_1}{t^5}+\frac {t}{12}+\frac {c_2}{t} \]