10.3.16 problem 20

Internal problem ID [1181]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.4. Page 76
Problem number : 20
Date solved : Monday, January 27, 2025 at 04:39:35 AM
CAS classification : [_Riccati]

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

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 31

dsolve(diff(y(t),t) = t-1-y(t)^2,y(t), singsol=all)
 

\[ y = \frac {\operatorname {AiryAi}\left (1, -1+t \right ) c_1 +\operatorname {AiryBi}\left (1, -1+t \right )}{\operatorname {AiryAi}\left (-1+t \right ) c_1 +\operatorname {AiryBi}\left (-1+t \right )} \]

✓ Solution by Mathematica

Time used: 0.127 (sec). Leaf size: 47

DSolve[D[y[t],t] == t-1-y[t]^2,y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to \frac {\operatorname {AiryBiPrime}(t-1)+c_1 \operatorname {AiryAiPrime}(t-1)}{\operatorname {AiryBi}(t-1)+c_1 \operatorname {AiryAi}(t-1)} \\ y(t)\to \frac {\operatorname {AiryAiPrime}(t-1)}{\operatorname {AiryAi}(t-1)} \\ \end{align*}