13.10.3 problem 3

Internal problem ID [2404]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 2.4, The method of variation of parameters. Page 154
Problem number : 3
Date solved : Monday, January 27, 2025 at 05:51:47 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} 2 y^{\prime \prime }-3 y^{\prime }+y&=\left (t^{2}+1\right ) {\mathrm e}^{t} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 31

dsolve(2*diff(y(t),t$2)-3*diff(y(t),t)+y(t)=(t^2+1)*exp(t),y(t), singsol=all)
 

\[ y = c_2 \,{\mathrm e}^{\frac {t}{2}}+\frac {{\mathrm e}^{t} \left (t^{3}-6 t^{2}+6 c_1 +27 t -54\right )}{3} \]

✓ Solution by Mathematica

Time used: 0.102 (sec). Leaf size: 39

DSolve[2*D[y[t],{t,2}]-3*D[y[t],t]+y[t]==(t^2+1)*Exp[t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^t \left (\frac {t^3}{3}-2 t^2+9 t-18+c_2\right )+c_1 e^{t/2} \]