14.5.2 problem 2

Internal problem ID [2539]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 1. First order differential equations. Section 1.17. What to do in practice. Excercises page 126
Problem number : 2
Date solved : Monday, January 27, 2025 at 05:59:43 AM
CAS classification : [_Riccati]

\begin{align*} y^{\prime }&=1-t +y^{2} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.109 (sec). Leaf size: 45

dsolve([diff(y(t),t)=1-t+y(t)^2,y(0) = 0],y(t), singsol=all)
 

\[ y = \frac {-\operatorname {AiryAi}\left (1, -1+t \right ) \operatorname {AiryBi}\left (1, -1\right )+\operatorname {AiryBi}\left (1, -1+t \right ) \operatorname {AiryAi}\left (1, -1\right )}{\operatorname {AiryAi}\left (-1+t \right ) \operatorname {AiryBi}\left (1, -1\right )-\operatorname {AiryBi}\left (-1+t \right ) \operatorname {AiryAi}\left (1, -1\right )} \]

✓ Solution by Mathematica

Time used: 0.165 (sec). Leaf size: 40

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

\[ y(t)\to \frac {\operatorname {AiryBiPrime}(-1) \operatorname {AiryAiPrime}(t-1)-\operatorname {AiryAiPrime}(-1) \operatorname {AiryBiPrime}(t-1)}{\operatorname {AiryAiPrime}(-1) \operatorname {AiryBi}(t-1)-\operatorname {AiryBiPrime}(-1) \operatorname {AiryAi}(t-1)} \]