74.3.26 problem 21

Internal problem ID [15886]
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 : 21
Date solved : Tuesday, January 28, 2025 at 08:17:19 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\frac {y}{\sqrt {-t^{2}+4}}&=t \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.250 (sec). Leaf size: 25

dsolve([diff(y(t),t)+y(t)/sqrt(4-t^2)=t,y(0) = 0],y(t), singsol=all)
 

\[ y = \left (\int _{0}^{t}\textit {\_z1} \,{\mathrm e}^{\arcsin \left (\frac {\textit {\_z1}}{2}\right )}d \textit {\_z1} \right ) {\mathrm e}^{-\arcsin \left (\frac {t}{2}\right )} \]

✓ Solution by Mathematica

Time used: 0.119 (sec). Leaf size: 52

DSolve[{D[y[t],t]+y[t]/Sqrt[4-t^2]==t,{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-\arctan \left (\frac {t}{\sqrt {4-t^2}}\right )} \int _0^te^{\arctan \left (\frac {K[1]}{\sqrt {4-K[1]^2}}\right )} K[1]dK[1] \]