Internal problem ID [14635]
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: 64.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {t^{2} \left (-1+\ln \left (t \right )\right ) y^{\prime \prime }-y^{\prime } t +y=-\frac {3 \left (\ln \left (t \right )+1\right )}{4 \sqrt {t}}} \] With initial conditions \begin {align*} [y \left (1\right ) = 0, y^{\prime }\left (1\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 20
dsolve([t^2*(ln(t)-1)*diff(y(t),t$2)-t*diff(y(t),t)+y(t)=-3/4*(1+ln(t))*1/sqrt(t),y(1) = 0, D(y)(1) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \left (-\frac {1}{t^{\frac {3}{2}}}-\frac {3 \ln \left (t \right )}{2 t}+1\right ) t \]
✓ Solution by Mathematica
Time used: 0.42 (sec). Leaf size: 20
DSolve[{t^2*(Log[t]-1)*y''[t]-t*y'[t]+y[t]==-3/4*(1+Log[t])*1/Sqrt[t],{y[1]==0,y'[1]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to t-\frac {1}{\sqrt {t}}-\frac {3 \log (t)}{2} \]