Internal problem ID [1686]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.4. Page 24
Problem number: 22.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {1+t -2 y+\left (4 t -3 y-6\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.297 (sec). Leaf size: 42
dsolve((1+t-2*y(t))+(4*t-3*y(t)-6)*diff(y(t),t)=0,y(t), singsol=all)
\[ y \relax (t ) = 2+\frac {\left (t -3\right ) \left (-c_{1} \RootOf \left (3 \left (t -3\right )^{4} c_{1} \textit {\_Z}^{20}-\textit {\_Z}^{4}-4\right )^{4}-c_{1}\right )}{3 c_{1}} \]
✓ Solution by Mathematica
Time used: 60.071 (sec). Leaf size: 1511
DSolve[(1+t-2*y[t])+(4*t-3*y[t]-6)*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {2}{3} (2 t-3)-\frac {1}{3 \text {Root}\left [\text {$\#$1}^5 \left (3125 e^{\frac {5 c_1}{9}} t^5-46875 e^{\frac {5 c_1}{9}} t^4+281250 e^{\frac {5 c_1}{9}} t^3-843750 e^{\frac {5 c_1}{9}} t^2+3125 t+1265625 e^{\frac {5 c_1}{9}} t-9375-759375 e^{\frac {5 c_1}{9}}\right )+\text {$\#$1}^4 \left (-3125 e^{\frac {5 c_1}{9}} t^4+37500 e^{\frac {5 c_1}{9}} t^3-168750 e^{\frac {5 c_1}{9}} t^2+337500 e^{\frac {5 c_1}{9}} t-3125-253125 e^{\frac {5 c_1}{9}}\right )+\text {$\#$1}^3 \left (1250 e^{\frac {5 c_1}{9}} t^3-11250 e^{\frac {5 c_1}{9}} t^2+33750 e^{\frac {5 c_1}{9}} t-33750 e^{\frac {5 c_1}{9}}\right )+\text {$\#$1}^2 \left (-250 e^{\frac {5 c_1}{9}} t^2+1500 e^{\frac {5 c_1}{9}} t-2250 e^{\frac {5 c_1}{9}}\right )+\text {$\#$1} \left (25 e^{\frac {5 c_1}{9}} t-75 e^{\frac {5 c_1}{9}}\right )-e^{\frac {5 c_1}{9}}\&,1\right ]} \\ y(t)\to \frac {2}{3} (2 t-3)-\frac {1}{3 \text {Root}\left [\text {$\#$1}^5 \left (3125 e^{\frac {5 c_1}{9}} t^5-46875 e^{\frac {5 c_1}{9}} t^4+281250 e^{\frac {5 c_1}{9}} t^3-843750 e^{\frac {5 c_1}{9}} t^2+3125 t+1265625 e^{\frac {5 c_1}{9}} t-9375-759375 e^{\frac {5 c_1}{9}}\right )+\text {$\#$1}^4 \left (-3125 e^{\frac {5 c_1}{9}} t^4+37500 e^{\frac {5 c_1}{9}} t^3-168750 e^{\frac {5 c_1}{9}} t^2+337500 e^{\frac {5 c_1}{9}} t-3125-253125 e^{\frac {5 c_1}{9}}\right )+\text {$\#$1}^3 \left (1250 e^{\frac {5 c_1}{9}} t^3-11250 e^{\frac {5 c_1}{9}} t^2+33750 e^{\frac {5 c_1}{9}} t-33750 e^{\frac {5 c_1}{9}}\right )+\text {$\#$1}^2 \left (-250 e^{\frac {5 c_1}{9}} t^2+1500 e^{\frac {5 c_1}{9}} t-2250 e^{\frac {5 c_1}{9}}\right )+\text {$\#$1} \left (25 e^{\frac {5 c_1}{9}} t-75 e^{\frac {5 c_1}{9}}\right )-e^{\frac {5 c_1}{9}}\&,2\right ]} \\ y(t)\to \frac {2}{3} (2 t-3)-\frac {1}{3 \text {Root}\left [\text {$\#$1}^5 \left (3125 e^{\frac {5 c_1}{9}} t^5-46875 e^{\frac {5 c_1}{9}} t^4+281250 e^{\frac {5 c_1}{9}} t^3-843750 e^{\frac {5 c_1}{9}} t^2+3125 t+1265625 e^{\frac {5 c_1}{9}} t-9375-759375 e^{\frac {5 c_1}{9}}\right )+\text {$\#$1}^4 \left (-3125 e^{\frac {5 c_1}{9}} t^4+37500 e^{\frac {5 c_1}{9}} t^3-168750 e^{\frac {5 c_1}{9}} t^2+337500 e^{\frac {5 c_1}{9}} t-3125-253125 e^{\frac {5 c_1}{9}}\right )+\text {$\#$1}^3 \left (1250 e^{\frac {5 c_1}{9}} t^3-11250 e^{\frac {5 c_1}{9}} t^2+33750 e^{\frac {5 c_1}{9}} t-33750 e^{\frac {5 c_1}{9}}\right )+\text {$\#$1}^2 \left (-250 e^{\frac {5 c_1}{9}} t^2+1500 e^{\frac {5 c_1}{9}} t-2250 e^{\frac {5 c_1}{9}}\right )+\text {$\#$1} \left (25 e^{\frac {5 c_1}{9}} t-75 e^{\frac {5 c_1}{9}}\right )-e^{\frac {5 c_1}{9}}\&,3\right ]} \\ y(t)\to \frac {2}{3} (2 t-3)-\frac {1}{3 \text {Root}\left [\text {$\#$1}^5 \left (3125 e^{\frac {5 c_1}{9}} t^5-46875 e^{\frac {5 c_1}{9}} t^4+281250 e^{\frac {5 c_1}{9}} t^3-843750 e^{\frac {5 c_1}{9}} t^2+3125 t+1265625 e^{\frac {5 c_1}{9}} t-9375-759375 e^{\frac {5 c_1}{9}}\right )+\text {$\#$1}^4 \left (-3125 e^{\frac {5 c_1}{9}} t^4+37500 e^{\frac {5 c_1}{9}} t^3-168750 e^{\frac {5 c_1}{9}} t^2+337500 e^{\frac {5 c_1}{9}} t-3125-253125 e^{\frac {5 c_1}{9}}\right )+\text {$\#$1}^3 \left (1250 e^{\frac {5 c_1}{9}} t^3-11250 e^{\frac {5 c_1}{9}} t^2+33750 e^{\frac {5 c_1}{9}} t-33750 e^{\frac {5 c_1}{9}}\right )+\text {$\#$1}^2 \left (-250 e^{\frac {5 c_1}{9}} t^2+1500 e^{\frac {5 c_1}{9}} t-2250 e^{\frac {5 c_1}{9}}\right )+\text {$\#$1} \left (25 e^{\frac {5 c_1}{9}} t-75 e^{\frac {5 c_1}{9}}\right )-e^{\frac {5 c_1}{9}}\&,4\right ]} \\ y(t)\to \frac {2}{3} (2 t-3)-\frac {1}{3 \text {Root}\left [\text {$\#$1}^5 \left (3125 e^{\frac {5 c_1}{9}} t^5-46875 e^{\frac {5 c_1}{9}} t^4+281250 e^{\frac {5 c_1}{9}} t^3-843750 e^{\frac {5 c_1}{9}} t^2+3125 t+1265625 e^{\frac {5 c_1}{9}} t-9375-759375 e^{\frac {5 c_1}{9}}\right )+\text {$\#$1}^4 \left (-3125 e^{\frac {5 c_1}{9}} t^4+37500 e^{\frac {5 c_1}{9}} t^3-168750 e^{\frac {5 c_1}{9}} t^2+337500 e^{\frac {5 c_1}{9}} t-3125-253125 e^{\frac {5 c_1}{9}}\right )+\text {$\#$1}^3 \left (1250 e^{\frac {5 c_1}{9}} t^3-11250 e^{\frac {5 c_1}{9}} t^2+33750 e^{\frac {5 c_1}{9}} t-33750 e^{\frac {5 c_1}{9}}\right )+\text {$\#$1}^2 \left (-250 e^{\frac {5 c_1}{9}} t^2+1500 e^{\frac {5 c_1}{9}} t-2250 e^{\frac {5 c_1}{9}}\right )+\text {$\#$1} \left (25 e^{\frac {5 c_1}{9}} t-75 e^{\frac {5 c_1}{9}}\right )-e^{\frac {5 c_1}{9}}\&,5\right ]} \\ \end{align*}