7.8 problem 18

Internal problem ID [5942]

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]]

Solve \begin {gather*} \boxed {2 y^{\prime \prime }+y^{\prime } t -2 y-10=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 0] \end {align*}

Solution by Maple

Time used: 0.062 (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)
 

\[ y \relax (t ) = \frac {5 t^{2}}{2} \]

Solution by Mathematica

Time used: 0.008 (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*}