Internal problem ID [5940]
Book: DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL,
WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th
edition.
Section: CHAPTER 7 THE LAPLACE TRANSFORM. 7.4.1 DERIVATIVES OF A TRANSFORM.
Page 309
Problem number: 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {t y^{\prime \prime }-y^{\prime }-2 t^{2}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 16
dsolve([t*diff(y(t),t$2)-diff(y(t),t)=2*t^2,y(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {t^{2} \left (4 t +3 c_{1} \right )}{6} \]
✓ Solution by Mathematica
Time used: 0.051 (sec). Leaf size: 26
DSolve[{y''[t]-y'[t]==2*t^2,{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\frac {2}{3} t (t (t+3)+6)+c_1 \left (e^t-1\right ) \\ \end{align*}