52.7.7 problem 17

Internal problem ID [8362]
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
Date solved : Monday, January 27, 2025 at 03:49:33 PM
CAS classification : [[_2nd_order, _missing_y]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.011 (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)
 

\[ y = \frac {t^{2} \left (4 t +3 c_{1} \right )}{6} \]

✓ Solution by Mathematica

Time used: 0.057 (sec). Leaf size: 29

DSolve[{D[y[t],{t,2}]-D[y[t],t]==2*t^2,{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -\frac {2 t^3}{3}-2 t^2-4 t+c_1 \left (e^t-1\right ) \]