14.2.20 problem 22
Internal
problem
ID
[2508]
Book
:
Differential
equations
and
their
applications,
4th
ed.,
M.
Braun
Section
:
Chapter
1.
First
order
differential
equations.
Section
1.4
separable
equations.
Excercises
page
24
Problem
number
:
22
Date
solved
:
Monday, January 27, 2025 at 05:56:27 AM
CAS
classification
:
[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\begin{align*} 1+t -2 y+\left (4 t -3 y-6\right ) y^{\prime }&=0 \end{align*}
✓ Solution by Maple
Time used: 0.318 (sec). Leaf size: 56
dsolve((1+t-2*y(t))+(4*t-3*y(t)-6)*diff(y(t),t)=0,y(t), singsol=all)
\[
y = \frac {\left (-t +3\right ) {\operatorname {RootOf}\left (-4+\left (3 c_1 \,t^{4}-36 c_1 \,t^{3}+162 c_1 \,t^{2}-324 c_1 t +243 c_1 \right ) \textit {\_Z}^{20}-\textit {\_Z}^{4}\right )}^{4}}{3}-\frac {t}{3}+3
\]
✓ Solution by Mathematica
Time used: 60.074 (sec). Leaf size: 1511
DSolve[(1+t-2*y[t])+(4*t-3*y[t]-6)*D[y[t],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*}