76.5.22 problem 23 (b)

Internal problem ID [17442]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.7 (Substitution Methods). Problems at page 108
Problem number : 23 (b)
Date solved : Tuesday, January 28, 2025 at 10:37:43 AM
CAS classification : [_Riccati]

\begin{align*} y^{\prime }+3 t y&=4-4 t^{2}+y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 55

dsolve(diff(y(t),t)+3*t*y(t)=4-4*t^2+y(t)^2,y(t), singsol=all)
 

\[ y = \frac {4 i \sqrt {10}\, \sqrt {\pi }\, \operatorname {erf}\left (\frac {i \sqrt {10}\, t}{2}\right ) t +40 c_{1} t +10 \,{\mathrm e}^{\frac {5 t^{2}}{2}}}{i \sqrt {\pi }\, \sqrt {10}\, \operatorname {erf}\left (\frac {i \sqrt {10}\, t}{2}\right )+10 c_{1}} \]

✓ Solution by Mathematica

Time used: 0.187 (sec). Leaf size: 52

DSolve[D[y[t],t]+3*t*y[t]==4-4*t^2+y[t]^2,y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to 4 t+\frac {e^{\frac {5 t^2}{2}}}{-\sqrt {\frac {\pi }{10}} \text {erfi}\left (\sqrt {\frac {5}{2}} t\right )+c_1} \\ y(t)\to 4 t \\ \end{align*}