Internal problem ID [14622]
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: 55.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {t^{2} y^{\prime \prime }+3 y^{\prime } t +y=\ln \left (t \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(t^2*diff(y(t),t$2)+3*t*diff(y(t),t)+y(t)=ln(t),y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (t +c_{1} \right ) \ln \left (t \right )-2 t +c_{2}}{t} \]
✓ Solution by Mathematica
Time used: 0.118 (sec). Leaf size: 22
DSolve[t^2*y''[t]+3*t*y'[t]+y[t]==Log[t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {-2 t+(t+c_2) \log (t)+c_1}{t} \]