Internal problem ID [14624]
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: 57.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {t^{2} y^{\prime \prime }-4 y^{\prime } t -6 y=2 \ln \left (t \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(t^2*diff(y(t),t$2)-4*t*diff(y(t),t)-6*y(t)=2*ln(t),y(t), singsol=all)
\[ y \left (t \right ) = t^{6} c_{2} -\frac {\ln \left (t \right )}{3}+\frac {5}{18}+\frac {c_{1}}{t} \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 27
DSolve[t^2*y''[t]-4*t*y'[t]-6*y[t]==2*Log[t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to c_2 t^6-\frac {\log (t)}{3}+\frac {c_1}{t}+\frac {5}{18} \]