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`]]
\[ \boxed {4 t y+\left (2 t^{2}+2 y\right ) y^{\prime }=-3 t^{2}} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.063 (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)
\[ y \left (t \right ) = -t^{2}+\sqrt {t^{4}-t^{3}+1} \]
✓ Solution by Mathematica
Time used: 0.164 (sec). Leaf size: 25
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]
\[ y(t)\to \sqrt {t^4-t^3+1}-t^2 \]