Internal problem ID [14385]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.5, page 64
Problem number: 42 (a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {-2 y+\left (4 t -3 y-6\right ) y^{\prime }=-1-t} \]
✓ Solution by Maple
Time used: 1.204 (sec). Leaf size: 56
dsolve((t-2*y(t)+1)+(4*t-3*y(t)-6)*diff(y(t),t)=0,y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (-t +3\right ) {\operatorname {RootOf}\left (-4+\left (3 c_{1} t^{4}-36 c_{1} t^{3}+162 c_{1} t^{2}-324 c_{1} t +243 c_{1} \right ) \textit {\_Z}^{20}-\textit {\_Z}^{4}\right )}^{4}}{3}-\frac {t}{3}+3 \]
✓ Solution by Mathematica
Time used: 60.07 (sec). Leaf size: 1511
DSolve[(t-2*y[t]+1)+(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*}