Internal problem ID [1662]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.2. Page 9
Problem number: 15.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y t +\left (t^{2}+1\right ) y^{\prime }-\left (t^{2}+1\right )^{\frac {5}{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(t*y(t)+(t^2+1)*diff(y(t),t) = (t^2+1)^(5/2),y(t), singsol=all)
\[ y \relax (t ) = \frac {\frac {1}{5} t^{5}+\frac {2}{3} t^{3}+t +c_{1}}{\sqrt {t^{2}+1}} \]
✓ Solution by Mathematica
Time used: 0.072 (sec). Leaf size: 36
DSolve[t*y[t]+(t^2+1)*y'[t] == (t^2+1)^(5/2),y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {3 t^5+10 t^3+15 t+15 c_1}{15 \sqrt {t^2+1}} \\ \end{align*}