Internal problem ID [1694]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.9. Page 66
Problem number: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational, [_1st_order, _with_symmetry_[F(x),G(x)]], [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {3 t^{2}+4 y t +\left (2 t^{2}+2 y\right ) y^{\prime }=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.041 (sec). Leaf size: 22
dsolve([3*t^2+4*t*y(t)+(2*t^2+2*y(t))*diff(y(t),t) = 0,y(0) = 1],y(t), singsol=all)
\[ y \relax (t ) = -t^{2}+\sqrt {t^{4}-t^{3}+1} \]
✓ Solution by Mathematica
Time used: 0.102 (sec). Leaf size: 24
DSolve[{3*t^2+4*t*y[t]+(2*t^2+2*y[t])*y'[t] == 0,y[0]==1},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \sqrt {(t-1) t^3+1}-t^2 \\ \end{align*}