73.6.18 problem 7.5 (h)
Internal
problem
ID
[15157]
Book
:
Ordinary
Differential
Equations.
An
introduction
to
the
fundamentals.
Kenneth
B.
Howell.
second
edition.
CRC
Press.
FL,
USA.
2020
Section
:
Chapter
7.
The
exact
form
and
general
integrating
fators.
Additional
exercises.
page
141
Problem
number
:
7.5
(h)
Date
solved
:
Tuesday, January 28, 2025 at 07:38:42 AM
CAS
classification
:
[[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class A`]]
\begin{align*} 4 y x +\left (3 x^{2}+5 y\right ) y^{\prime }&=0 \end{align*}
✓ Solution by Maple
Time used: 2.086 (sec). Leaf size: 29
dsolve(4*x*y(x)+(3*x^2+5*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[
y = \operatorname {RootOf}\left (x^{5} \textit {\_Z}^{25}+x^{5} \textit {\_Z}^{15}-c_{1} \right )^{10} x^{2}
\]
✓ Solution by Mathematica
Time used: 60.071 (sec). Leaf size: 1121
DSolve[4*x*y[x]+(3*x^2+5*y[x])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*}
y(x)\to -\frac {3 x^2}{5}+\frac {1}{5 \text {Root}\left [\text {$\#$1}^{10} \left (11664 x^{20}+11664 e^{60 c_1}\right )-9720 \text {$\#$1}^8 x^{16}+1080 \text {$\#$1}^7 x^{14}+3105 \text {$\#$1}^6 x^{12}-666 \text {$\#$1}^5 x^{10}-425 \text {$\#$1}^4 x^8+140 \text {$\#$1}^3 x^6+15 \text {$\#$1}^2 x^4-10 \text {$\#$1} x^2+1\&,1\right ]} \\
y(x)\to -\frac {3 x^2}{5}+\frac {1}{5 \text {Root}\left [\text {$\#$1}^{10} \left (11664 x^{20}+11664 e^{60 c_1}\right )-9720 \text {$\#$1}^8 x^{16}+1080 \text {$\#$1}^7 x^{14}+3105 \text {$\#$1}^6 x^{12}-666 \text {$\#$1}^5 x^{10}-425 \text {$\#$1}^4 x^8+140 \text {$\#$1}^3 x^6+15 \text {$\#$1}^2 x^4-10 \text {$\#$1} x^2+1\&,2\right ]} \\
y(x)\to -\frac {3 x^2}{5}+\frac {1}{5 \text {Root}\left [\text {$\#$1}^{10} \left (11664 x^{20}+11664 e^{60 c_1}\right )-9720 \text {$\#$1}^8 x^{16}+1080 \text {$\#$1}^7 x^{14}+3105 \text {$\#$1}^6 x^{12}-666 \text {$\#$1}^5 x^{10}-425 \text {$\#$1}^4 x^8+140 \text {$\#$1}^3 x^6+15 \text {$\#$1}^2 x^4-10 \text {$\#$1} x^2+1\&,3\right ]} \\
y(x)\to -\frac {3 x^2}{5}+\frac {1}{5 \text {Root}\left [\text {$\#$1}^{10} \left (11664 x^{20}+11664 e^{60 c_1}\right )-9720 \text {$\#$1}^8 x^{16}+1080 \text {$\#$1}^7 x^{14}+3105 \text {$\#$1}^6 x^{12}-666 \text {$\#$1}^5 x^{10}-425 \text {$\#$1}^4 x^8+140 \text {$\#$1}^3 x^6+15 \text {$\#$1}^2 x^4-10 \text {$\#$1} x^2+1\&,4\right ]} \\
y(x)\to -\frac {3 x^2}{5}+\frac {1}{5 \text {Root}\left [\text {$\#$1}^{10} \left (11664 x^{20}+11664 e^{60 c_1}\right )-9720 \text {$\#$1}^8 x^{16}+1080 \text {$\#$1}^7 x^{14}+3105 \text {$\#$1}^6 x^{12}-666 \text {$\#$1}^5 x^{10}-425 \text {$\#$1}^4 x^8+140 \text {$\#$1}^3 x^6+15 \text {$\#$1}^2 x^4-10 \text {$\#$1} x^2+1\&,5\right ]} \\
y(x)\to -\frac {3 x^2}{5}+\frac {1}{5 \text {Root}\left [\text {$\#$1}^{10} \left (11664 x^{20}+11664 e^{60 c_1}\right )-9720 \text {$\#$1}^8 x^{16}+1080 \text {$\#$1}^7 x^{14}+3105 \text {$\#$1}^6 x^{12}-666 \text {$\#$1}^5 x^{10}-425 \text {$\#$1}^4 x^8+140 \text {$\#$1}^3 x^6+15 \text {$\#$1}^2 x^4-10 \text {$\#$1} x^2+1\&,6\right ]} \\
y(x)\to -\frac {3 x^2}{5}+\frac {1}{5 \text {Root}\left [\text {$\#$1}^{10} \left (11664 x^{20}+11664 e^{60 c_1}\right )-9720 \text {$\#$1}^8 x^{16}+1080 \text {$\#$1}^7 x^{14}+3105 \text {$\#$1}^6 x^{12}-666 \text {$\#$1}^5 x^{10}-425 \text {$\#$1}^4 x^8+140 \text {$\#$1}^3 x^6+15 \text {$\#$1}^2 x^4-10 \text {$\#$1} x^2+1\&,7\right ]} \\
y(x)\to -\frac {3 x^2}{5}+\frac {1}{5 \text {Root}\left [\text {$\#$1}^{10} \left (11664 x^{20}+11664 e^{60 c_1}\right )-9720 \text {$\#$1}^8 x^{16}+1080 \text {$\#$1}^7 x^{14}+3105 \text {$\#$1}^6 x^{12}-666 \text {$\#$1}^5 x^{10}-425 \text {$\#$1}^4 x^8+140 \text {$\#$1}^3 x^6+15 \text {$\#$1}^2 x^4-10 \text {$\#$1} x^2+1\&,8\right ]} \\
y(x)\to -\frac {3 x^2}{5}+\frac {1}{5 \text {Root}\left [\text {$\#$1}^{10} \left (11664 x^{20}+11664 e^{60 c_1}\right )-9720 \text {$\#$1}^8 x^{16}+1080 \text {$\#$1}^7 x^{14}+3105 \text {$\#$1}^6 x^{12}-666 \text {$\#$1}^5 x^{10}-425 \text {$\#$1}^4 x^8+140 \text {$\#$1}^3 x^6+15 \text {$\#$1}^2 x^4-10 \text {$\#$1} x^2+1\&,9\right ]} \\
y(x)\to -\frac {3 x^2}{5}+\frac {1}{5 \text {Root}\left [\text {$\#$1}^{10} \left (11664 x^{20}+11664 e^{60 c_1}\right )-9720 \text {$\#$1}^8 x^{16}+1080 \text {$\#$1}^7 x^{14}+3105 \text {$\#$1}^6 x^{12}-666 \text {$\#$1}^5 x^{10}-425 \text {$\#$1}^4 x^8+140 \text {$\#$1}^3 x^6+15 \text {$\#$1}^2 x^4-10 \text {$\#$1} x^2+1\&,10\right ]} \\
\end{align*}