76.12.4 problem 4

Internal problem ID [17560]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.2 (Theory of second order linear homogeneous equations). Problems at page 226
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 10:43:59 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+\cos \left (t \right ) y^{\prime }+3 \ln \left (t \right ) y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (2\right )&=3\\ y^{\prime }\left (2\right )&=1 \end{align*}

✗ Solution by Maple

dsolve([diff(y(t),t$2)+cos(t)*diff(y(t),t)+3*ln(t)*y(t)=0,y(2) = 3, D(y)(2) = 1],y(t), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

DSolve[{D[y[t],{t,2}]+Cos[t]*D[y[t],t]+3*Log[t]*y[t]==0,{y[2]==3,Derivative[1][y][2]==1}},y[t],t,IncludeSingularSolutions -> True]
 

Not solved