Internal problem ID [4460]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson
2018.
Section: Chapter 2, First order differential equations. Section 2.3, Linear equations. Exercises. page
54
Problem number: 19.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {t^{2} x^{\prime }+3 x t -t^{4} \ln \relax (t )-1=0} \end {gather*} With initial conditions \begin {align*} [x \relax (1) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 28
dsolve([t^2*diff(x(t),t)+3*t*x(t)=t^4*ln(t)+1,x(1) = 0],x(t), singsol=all)
\[ x \relax (t ) = \frac {6 t^{6} \ln \relax (t )-t^{6}+18 t^{2}-17}{36 t^{3}} \]
✓ Solution by Mathematica
Time used: 0.06 (sec). Leaf size: 29
DSolve[{t^2*x'[t]+3*t*x[t]==t^4*Log[t]+1,{x[1]==0}},x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -\frac {t^6-6 t^6 \log (t)-18 t^2+17}{36 t^3} \\ \end{align*}