57.3.11 problem 11

Internal problem ID [9068]
Book : First order enumerated odes
Section : section 3. First order odes solved using Laplace method
Problem number : 11
Date solved : Monday, January 27, 2025 at 05:31:52 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*}

✓ Solution by Maple

Time used: 1.098 (sec). Leaf size: 40

dsolve([diff(y(t),t)+t^2*y(t)=0,y(0) = 0],y(t), singsol=all)
 

\[ y = -\frac {c_{2} \mathcal {L}^{-1}\left (\operatorname {AiryBi}\left (-\textit {\_s1} \right ), \textit {\_s1} , 0\right ) \mathcal {L}^{-1}\left (\operatorname {AiryAi}\left (-\textit {\_s1} \right ), \textit {\_s1} , t\right )}{\mathcal {L}^{-1}\left (\operatorname {AiryAi}\left (-\textit {\_s1} \right ), \textit {\_s1} , 0\right )}+c_{2} \mathcal {L}^{-1}\left (\operatorname {AiryBi}\left (-\textit {\_s1} \right ), \textit {\_s1} , t\right ) \]

✓ Solution by Mathematica

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

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

\[ y(t)\to 0 \]