Internal problem ID [14473]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.1, page 141
Problem number: 47.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+b \left (t \right ) y^{\prime }+c \left (t \right ) y=0} \] Given that one solution of the ode is \begin {align*} y_1 &= \frac {\cos \left (t \right )}{t^{3}} \end {align*}
With initial conditions \begin {align*} [y \left (\pi \right ) = 0, y^{\prime }\left (2 \pi \right ) = 0] \end {align*}
✗ Solution by Maple
dsolve([diff(diff(y(t),t),t)+b(t)*diff(y(t),t)+c(t)*y(t) = 0, 1/t^3*cos(t), y(Pi) = 0, D(y)(2*Pi) = 0], singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y''[t]+b[t]*y'[t]+c[t]*y[t]==0,{y[Pi]==0,y'[2*Pi]==0},y[t],t,IncludeSingularSolutions -> True]
Not solved