10.10.20 problem 30

Internal problem ID [1352]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, section 3.6, Variation of Parameters. page 190
Problem number : 30
Date solved : Monday, January 27, 2025 at 04:52:04 AM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.001 (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: 0.015 (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]
 

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