Internal problem ID [14636]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.4, page 163
Problem number: 65.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (-\cos \left (t \right ) t +\sin \left (t \right )\right ) y^{\prime \prime }-t \sin \left (t \right ) y^{\prime }+\sin \left (t \right ) y=t} \] With initial conditions \begin {align*} \left [y \left (\frac {\pi }{4}\right ) = 0, y^{\prime }\left (\frac {\pi }{4}\right ) = 0\right ] \end {align*}
✓ Solution by Maple
Time used: 0.156 (sec). Leaf size: 29
dsolve([(sin(t)-t*cos(t))*diff(y(t),t$2)-t*sin(t)*diff(y(t),t)+sin(t)*y(t)=t,y(1/4*Pi) = 0, D(y)(1/4*Pi) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {-4 \sqrt {2}\, t +\left (-4+\pi \right ) \cos \left (t \right )+\left (\pi +4\right ) \sin \left (t \right )}{-4+\pi } \]
✓ Solution by Mathematica
Time used: 1.047 (sec). Leaf size: 32
DSolve[{(Sin[t]-t*Cos[t])*y''[t]-t*Sin[t]*y'[t]+Sin[t]*y[t]==t,{y[Pi/4]==0,y'[Pi/4]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {-4 \sqrt {2} t+(4+\pi ) \sin (t)+(\pi -4) \cos (t)}{\pi -4} \]