Internal problem ID [11676]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 9, First order linear equations and the integrating factor. Exercises page
86
Problem number: 9.1 (ii).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {t x+x^{\prime }=4 t} \] With initial conditions \begin {align*} [x \left (0\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve([diff(x(t),t)+t*x(t)=4*t,x(0) = 2],x(t), singsol=all)
\[ x \left (t \right ) = 4-2 \,{\mathrm e}^{-\frac {t^{2}}{2}} \]
✓ Solution by Mathematica
Time used: 0.066 (sec). Leaf size: 18
DSolve[{x'[t]+t*x[t]==4*t,{x[0]==2}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to 4-2 e^{-\frac {t^2}{2}} \]