67.5.1 problem Problem 1(a)

Internal problem ID [14087]
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(a)
Date solved : Tuesday, January 28, 2025 at 06:14:06 AM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} t^{2} y^{\prime \prime }+3 y^{\prime } t +y&=t^{7} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 22

dsolve(t^2*diff(y(t),t$2)+3*t*diff(y(t),t)+y(t)=t^7,y(t), singsol=all)
 

\[ y = \frac {c_{2}}{t}+\frac {t^{7}}{64}+\frac {c_{1} \ln \left (t \right )}{t} \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 26

DSolve[t^2*D[y[t],{t,2}]+3*t*D[y[t],t]+y[t]==t^7,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {t^8+64 c_2 \log (t)+64 c_1}{64 t} \]