46.7.8 problem 18

Internal problem ID [9649]
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 : Tuesday, September 30, 2025 at 06:21:51 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*}

✓ Maple. Time used: 0.029 (sec). Leaf size: 9

ode:=2*diff(diff(y(t),t),t)+t*diff(y(t),t)-2*y(t) = 10; 
ic:=[y(0) = 0, D(y)(0) = 0]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 10

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

\begin{align*} y(t)&\to 5 t^2 \end{align*}

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t*Derivative(y(t), t) - 2*y(t) + 2*Derivative(y(t), (t, 2)) - 10,0) 
ics = {y(0): 0, Subs(Derivative(y(t), t), t, 0): 0} 
dsolve(ode,func=y(t),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(t), t) - 2*(y(t) - Derivative(y(t), (t, 2)) + 5)/t cannot be solved by the factorable group method