Internal problem ID [13832]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.1, page 32
Problem number: 22.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }+\frac {y}{\sqrt {-t^{2}+4}}=t} \] With initial conditions \begin {align*} [y \left (3\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 31
dsolve([diff(y(t),t)+y(t)/sqrt(4-t^2)=t,y(3) = -1],y(t), singsol=all)
\[ y = \left (\int _{3}^{t}\textit {\_z1} \,{\mathrm e}^{\arcsin \left (\frac {\textit {\_z1}}{2}\right )}d \textit {\_z1} -{\mathrm e}^{\arcsin \left (\frac {3}{2}\right )}\right ) {\mathrm e}^{-\arcsin \left (\frac {t}{2}\right )} \]
✓ Solution by Mathematica
Time used: 0.085 (sec). Leaf size: 88
DSolve[{y'[t]+y[t]/Sqrt[4-t^2]==t,{y[3]==-1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{2 \arctan \left (\frac {\sqrt {4-t^2}}{t+2}\right )-2 i \text {arctanh}\left (\frac {1}{\sqrt {5}}\right )} \left (-1+e^{2 i \text {arctanh}\left (\frac {1}{\sqrt {5}}\right )} \int _3^te^{-2 \arctan \left (\frac {\sqrt {4-K[1]^2}}{K[1]+2}\right )} K[1]dK[1]\right ) \]