10.10.14 problem 14

Internal problem ID [1346]
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 : 14
Date solved : Monday, January 27, 2025 at 04:51:52 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y&=2 t^{3} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 15

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

\[ y = t \left ({\mathrm e}^{t} c_1 +c_2 -2 t \right ) \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 20

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

\[ y(t)\to t \left (-2 t+c_2 e^t-2+c_1\right ) \]