Internal problem ID [1665]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.2. Page 9
Problem number: 21.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }+\frac {y}{\sqrt {t}}-{\mathrm e}^{\frac {\sqrt {t}}{2}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 32
dsolve(diff(y(t),t)+1/sqrt(t)*y(t)=exp(sqrt(t)/2),y(t), singsol=all)
\[ y \left (t \right ) = \left (\frac {4 \,{\mathrm e}^{\frac {5 \sqrt {t}}{2}} \sqrt {t}}{5}-\frac {8 \,{\mathrm e}^{\frac {5 \sqrt {t}}{2}}}{25}+c_{1} \right ) {\mathrm e}^{-2 \sqrt {t}} \]
✓ Solution by Mathematica
Time used: 0.091 (sec). Leaf size: 42
DSolve[y'[t]+1/Sqrt[t]*y[t]==Exp[Sqrt[t]/2],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {4}{25} e^{\frac {\sqrt {t}}{2}} \left (5 \sqrt {t}-2\right )+c_1 e^{-2 \sqrt {t}} \\ \end{align*}