Internal problem ID [13850]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 27. Differentiation and the Laplace transform. Additional Exercises. page
496
Problem number: 27.1 (b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }-2 y=t^{3}} \] With initial conditions \begin {align*} [y \left (0\right ) = 4] \end {align*}
✓ Solution by Maple
Time used: 4.172 (sec). Leaf size: 25
dsolve([diff(y(t),t)-2*y(t)=t^3,y(0) = 4],y(t), singsol=all)
\[ y \left (t \right ) = -\frac {3 t}{4}-\frac {t^{3}}{2}-\frac {3 t^{2}}{4}+\frac {35 \,{\mathrm e}^{2 t}}{8}-\frac {3}{8} \]
✓ Solution by Mathematica
Time used: 0.052 (sec). Leaf size: 31
DSolve[{y'[t]+4*y[t]==t^3,{y[0]==4}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{128} \left (32 t^3-24 t^2+12 t+515 e^{-4 t}-3\right ) \]