14.10.10 problem 10

Internal problem ID [2592]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 2. Second order differential equations. Section 2.4. The method of variation of parameters. Excercises page 156
Problem number : 10
Date solved : Monday, January 27, 2025 at 06:01:33 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+p \left (t \right ) y^{\prime }+q \left (t \right ) y&=1+t \end{align*}

Using reduction of order method given that one solution is

\begin{align*} y&=\left (1+t \right )^{2} \end{align*}

✗ Solution by Maple

dsolve([diff(y(t),t$2)+p(t)*diff(y(t),t)+q(t)*y(t)=1+t,(1+t)^2],singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[D[y[t],{t,2}]+p[t]*D[y[t],t]+q[t]*y[t]==1+t,y[t],t,IncludeSingularSolutions -> True]
 

Not solved