Internal problem ID [5941]
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: 18.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {2 y^{\prime \prime }+t y^{\prime }-2 y-10=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 9
dsolve([2*diff(y(t),t$2)+t*diff(y(t),t)-2*y(t)=10,y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {5 t^{2}}{2} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 10
DSolve[{y''[t]+t*y'[t]-2*y[t]==10,{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to 5 t^2 \\ \end{align*}