Internal problem ID [1663]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.2. Page 9
Problem number: 16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {4 y t +\left (t^{2}+1\right ) y^{\prime }-t=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 15
dsolve([4*t*y(t)+(t^2+1)*diff(y(t),t) = t,y(0) = 0],y(t), singsol=all)
\[ y \relax (t ) = \frac {t^{2} \left (t^{2}+2\right )}{4 \left (t^{2}+1\right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.032 (sec). Leaf size: 20
DSolve[{4*t*y[t]+(t^2+1)*y'[t]== t,y[0]==0},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{4}-\frac {1}{4 \left (t^2+1\right )^2} \\ \end{align*}