52.7.8 problem 18

Internal problem ID [8363]
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
Date solved : Monday, January 27, 2025 at 03:49:35 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 y^{\prime \prime }+t y^{\prime }-2 y&=10 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.040 (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)
 

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

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 10

DSolve[{D[y[t],{t,2}]+t*D[y[t],t]-2*y[t]==10,{y[0]==0,Derivative[1][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 5 t^2 \]