Internal problem ID [531]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.4. Page 76
Problem number: 20.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
\[ \boxed {y^{\prime }+y^{2}=-1+t} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(diff(y(t),t) = t-1-y(t)^2,y(t), singsol=all)
\[ y \left (t \right ) = \frac {\operatorname {AiryAi}\left (1, t -1\right ) c_{1} +\operatorname {AiryBi}\left (1, t -1\right )}{\operatorname {AiryAi}\left (t -1\right ) c_{1} +\operatorname {AiryBi}\left (t -1\right )} \]
✓ Solution by Mathematica
Time used: 0.123 (sec). Leaf size: 47
DSolve[y'[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*}