7.5.60 problem 60
Internal
problem
ID
[164]
Book
:
Elementary
Differential
Equations.
By
C.
Henry
Edwards,
David
E.
Penney
and
David
Calvis.
6th
edition.
2008
Section
:
Chapter
1.
First
order
differential
equations.
Section
1.6
(substitution
and
exact
equations).
Problems
at
page
72
Problem
number
:
60
Date
solved
:
Friday, February 07, 2025 at 07:59:29 AM
CAS
classification
:
[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\begin{align*} y^{\prime }&=\frac {2 y-x +7}{4 x -3 y-18} \end{align*}
✓ Solution by Maple
Time used: 1.154 (sec). Leaf size: 56
dsolve(diff(y(x),x)= (2*y(x)-x+7)/(4*x-3*y(x)-18),y(x), singsol=all)
\[
y = \frac {\left (-x +3\right ) {\operatorname {RootOf}\left (-4+\left (3 c_1 \,x^{4}-36 c_1 \,x^{3}+162 c_1 \,x^{2}-324 c_1 x +243 c_1 \right ) \textit {\_Z}^{20}-\textit {\_Z}^{4}\right )}^{4}}{3}-1-\frac {x}{3}
\]
✓ Solution by Mathematica
Time used: 60.066 (sec). Leaf size: 1511
DSolve[D[y[x],x]==(2*y[x]-x+7)/(4*x-3*y[x]-18),y[x],x,IncludeSingularSolutions -> True]
\begin{align*}
y(x)\to \frac {2}{3} (2 x-9)-\frac {1}{3 \text {Root}\left [\text {$\#$1}^5 \left (3125 e^{\frac {5 c_1}{9}} x^5-46875 e^{\frac {5 c_1}{9}} x^4+281250 e^{\frac {5 c_1}{9}} x^3-843750 e^{\frac {5 c_1}{9}} x^2+3125 x+1265625 e^{\frac {5 c_1}{9}} x-9375-759375 e^{\frac {5 c_1}{9}}\right )+\text {$\#$1}^4 \left (-3125 e^{\frac {5 c_1}{9}} x^4+37500 e^{\frac {5 c_1}{9}} x^3-168750 e^{\frac {5 c_1}{9}} x^2+337500 e^{\frac {5 c_1}{9}} x-3125-253125 e^{\frac {5 c_1}{9}}\right )+\text {$\#$1}^3 \left (1250 e^{\frac {5 c_1}{9}} x^3-11250 e^{\frac {5 c_1}{9}} x^2+33750 e^{\frac {5 c_1}{9}} x-33750 e^{\frac {5 c_1}{9}}\right )+\text {$\#$1}^2 \left (-250 e^{\frac {5 c_1}{9}} x^2+1500 e^{\frac {5 c_1}{9}} x-2250 e^{\frac {5 c_1}{9}}\right )+\text {$\#$1} \left (25 e^{\frac {5 c_1}{9}} x-75 e^{\frac {5 c_1}{9}}\right )-e^{\frac {5 c_1}{9}}\&,1\right ]} \\
y(x)\to \frac {2}{3} (2 x-9)-\frac {1}{3 \text {Root}\left [\text {$\#$1}^5 \left (3125 e^{\frac {5 c_1}{9}} x^5-46875 e^{\frac {5 c_1}{9}} x^4+281250 e^{\frac {5 c_1}{9}} x^3-843750 e^{\frac {5 c_1}{9}} x^2+3125 x+1265625 e^{\frac {5 c_1}{9}} x-9375-759375 e^{\frac {5 c_1}{9}}\right )+\text {$\#$1}^4 \left (-3125 e^{\frac {5 c_1}{9}} x^4+37500 e^{\frac {5 c_1}{9}} x^3-168750 e^{\frac {5 c_1}{9}} x^2+337500 e^{\frac {5 c_1}{9}} x-3125-253125 e^{\frac {5 c_1}{9}}\right )+\text {$\#$1}^3 \left (1250 e^{\frac {5 c_1}{9}} x^3-11250 e^{\frac {5 c_1}{9}} x^2+33750 e^{\frac {5 c_1}{9}} x-33750 e^{\frac {5 c_1}{9}}\right )+\text {$\#$1}^2 \left (-250 e^{\frac {5 c_1}{9}} x^2+1500 e^{\frac {5 c_1}{9}} x-2250 e^{\frac {5 c_1}{9}}\right )+\text {$\#$1} \left (25 e^{\frac {5 c_1}{9}} x-75 e^{\frac {5 c_1}{9}}\right )-e^{\frac {5 c_1}{9}}\&,2\right ]} \\
y(x)\to \frac {2}{3} (2 x-9)-\frac {1}{3 \text {Root}\left [\text {$\#$1}^5 \left (3125 e^{\frac {5 c_1}{9}} x^5-46875 e^{\frac {5 c_1}{9}} x^4+281250 e^{\frac {5 c_1}{9}} x^3-843750 e^{\frac {5 c_1}{9}} x^2+3125 x+1265625 e^{\frac {5 c_1}{9}} x-9375-759375 e^{\frac {5 c_1}{9}}\right )+\text {$\#$1}^4 \left (-3125 e^{\frac {5 c_1}{9}} x^4+37500 e^{\frac {5 c_1}{9}} x^3-168750 e^{\frac {5 c_1}{9}} x^2+337500 e^{\frac {5 c_1}{9}} x-3125-253125 e^{\frac {5 c_1}{9}}\right )+\text {$\#$1}^3 \left (1250 e^{\frac {5 c_1}{9}} x^3-11250 e^{\frac {5 c_1}{9}} x^2+33750 e^{\frac {5 c_1}{9}} x-33750 e^{\frac {5 c_1}{9}}\right )+\text {$\#$1}^2 \left (-250 e^{\frac {5 c_1}{9}} x^2+1500 e^{\frac {5 c_1}{9}} x-2250 e^{\frac {5 c_1}{9}}\right )+\text {$\#$1} \left (25 e^{\frac {5 c_1}{9}} x-75 e^{\frac {5 c_1}{9}}\right )-e^{\frac {5 c_1}{9}}\&,3\right ]} \\
y(x)\to \frac {2}{3} (2 x-9)-\frac {1}{3 \text {Root}\left [\text {$\#$1}^5 \left (3125 e^{\frac {5 c_1}{9}} x^5-46875 e^{\frac {5 c_1}{9}} x^4+281250 e^{\frac {5 c_1}{9}} x^3-843750 e^{\frac {5 c_1}{9}} x^2+3125 x+1265625 e^{\frac {5 c_1}{9}} x-9375-759375 e^{\frac {5 c_1}{9}}\right )+\text {$\#$1}^4 \left (-3125 e^{\frac {5 c_1}{9}} x^4+37500 e^{\frac {5 c_1}{9}} x^3-168750 e^{\frac {5 c_1}{9}} x^2+337500 e^{\frac {5 c_1}{9}} x-3125-253125 e^{\frac {5 c_1}{9}}\right )+\text {$\#$1}^3 \left (1250 e^{\frac {5 c_1}{9}} x^3-11250 e^{\frac {5 c_1}{9}} x^2+33750 e^{\frac {5 c_1}{9}} x-33750 e^{\frac {5 c_1}{9}}\right )+\text {$\#$1}^2 \left (-250 e^{\frac {5 c_1}{9}} x^2+1500 e^{\frac {5 c_1}{9}} x-2250 e^{\frac {5 c_1}{9}}\right )+\text {$\#$1} \left (25 e^{\frac {5 c_1}{9}} x-75 e^{\frac {5 c_1}{9}}\right )-e^{\frac {5 c_1}{9}}\&,4\right ]} \\
y(x)\to \frac {2}{3} (2 x-9)-\frac {1}{3 \text {Root}\left [\text {$\#$1}^5 \left (3125 e^{\frac {5 c_1}{9}} x^5-46875 e^{\frac {5 c_1}{9}} x^4+281250 e^{\frac {5 c_1}{9}} x^3-843750 e^{\frac {5 c_1}{9}} x^2+3125 x+1265625 e^{\frac {5 c_1}{9}} x-9375-759375 e^{\frac {5 c_1}{9}}\right )+\text {$\#$1}^4 \left (-3125 e^{\frac {5 c_1}{9}} x^4+37500 e^{\frac {5 c_1}{9}} x^3-168750 e^{\frac {5 c_1}{9}} x^2+337500 e^{\frac {5 c_1}{9}} x-3125-253125 e^{\frac {5 c_1}{9}}\right )+\text {$\#$1}^3 \left (1250 e^{\frac {5 c_1}{9}} x^3-11250 e^{\frac {5 c_1}{9}} x^2+33750 e^{\frac {5 c_1}{9}} x-33750 e^{\frac {5 c_1}{9}}\right )+\text {$\#$1}^2 \left (-250 e^{\frac {5 c_1}{9}} x^2+1500 e^{\frac {5 c_1}{9}} x-2250 e^{\frac {5 c_1}{9}}\right )+\text {$\#$1} \left (25 e^{\frac {5 c_1}{9}} x-75 e^{\frac {5 c_1}{9}}\right )-e^{\frac {5 c_1}{9}}\&,5\right ]} \\
\end{align*}