56.1.47 problem 47

Internal problem ID [8759]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 47
Date solved : Monday, January 27, 2025 at 04:48:22 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} t y^{\prime \prime }+4 y^{\prime }&=t^{2} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 17

dsolve(t*diff(y(t),t$2)+4*diff(y(t),t)=t^2,y(t), singsol=all)
 

\[ y = \frac {t^{3}}{18}-\frac {c_{1}}{3 t^{3}}+c_{2} \]

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 24

DSolve[t*D[y[t],{t,2}]+4*D[y[t],t]==t^2,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {t^3}{18}-\frac {c_1}{3 t^3}+c_2 \]