51.3.11 problem 11

Internal problem ID [10354]
Book : First order enumerated odes
Section : section 3. First order odes solved using Laplace method
Problem number : 11
Date solved : Tuesday, September 30, 2025 at 07:22:32 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }+t^{2} y&=0 \end{align*}

Using Laplace method With initial conditions

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

✓ Maple. Time used: 0.120 (sec). Leaf size: 40

ode:=diff(y(t),t)+t^2*y(t) = 0; 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

\[ y = -\frac {c_2 \mathcal {L}^{-1}\left (\operatorname {AiryBi}\left (-\textit {\_s1} \right ), \textit {\_s1} , 0\right ) \mathcal {L}^{-1}\left (\operatorname {AiryAi}\left (-\textit {\_s1} \right ), \textit {\_s1} , t\right )}{\mathcal {L}^{-1}\left (\operatorname {AiryAi}\left (-\textit {\_s1} \right ), \textit {\_s1} , 0\right )}+c_2 \mathcal {L}^{-1}\left (\operatorname {AiryBi}\left (-\textit {\_s1} \right ), \textit {\_s1} , t\right ) \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 6

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

\begin{align*} y(t)&\to 0 \end{align*}

✓ Sympy. Time used: 0.165 (sec). Leaf size: 3

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

\[ y{\left (t \right )} = 0 \]