47.2.39 problem 37
Internal
problem
ID
[7455]
Book
:
Ordinary
differential
equations
and
calculus
of
variations.
Makarets
and
Reshetnyak.
Wold
Scientific.
Singapore.
1995
Section
:
Chapter
1.
First
order
differential
equations.
Section
1.2
Homogeneous
equations
problems.
page
12
Problem
number
:
37
Date
solved
:
Monday, January 27, 2025 at 03:00:35 PM
CAS
classification
:
[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\begin{align*} \left (x +4 y\right ) y^{\prime }&=2 x +3 y-5 \end{align*}
✓ Solution by Maple
Time used: 0.227 (sec). Leaf size: 186
dsolve((x+4*y(x))*diff(y(x),x)=2*x+3*y(x)-5,y(x), singsol=all)
\[
y = \frac {\left (x -5\right ) \operatorname {RootOf}\left (\textit {\_Z}^{36}+\left (3 c_{1} x^{6}-72 c_{1} x^{5}+720 c_{1} x^{4}-3840 c_{1} x^{3}+11520 c_{1} x^{2}-18432 c_{1} x +12288 c_{1} \right ) \textit {\_Z}^{6}-2 c_{1} x^{6}+48 c_{1} x^{5}-480 c_{1} x^{4}+2560 c_{1} x^{3}-7680 c_{1} x^{2}+12288 c_{1} x -8192 c_{1} \right )^{6}-x +4}{\operatorname {RootOf}\left (\textit {\_Z}^{36}+\left (3 c_{1} x^{6}-72 c_{1} x^{5}+720 c_{1} x^{4}-3840 c_{1} x^{3}+11520 c_{1} x^{2}-18432 c_{1} x +12288 c_{1} \right ) \textit {\_Z}^{6}-2 c_{1} x^{6}+48 c_{1} x^{5}-480 c_{1} x^{4}+2560 c_{1} x^{3}-7680 c_{1} x^{2}+12288 c_{1} x -8192 c_{1} \right )^{6}}
\]
✓ Solution by Mathematica
Time used: 60.047 (sec). Leaf size: 805
DSolve[(x+4*y[x])*D[y[x],x]==2*x+3*y[x]-5,y[x],x,IncludeSingularSolutions -> True]
\begin{align*}
y(x)\to -\frac {x}{4}+\frac {1}{4 \text {Root}\left [\text {$\#$1}^6 \left (-3125 x^6+75000 x^5-750000 x^4+4000000 x^3-12000000 x^2+19200000 x-12800000+3125 e^{\frac {15 c_1}{8}}\right )+\text {$\#$1}^4 \left (1875 x^4-30000 x^3+180000 x^2-480000 x+480000\right )+\text {$\#$1}^3 \left (-1000 x^3+12000 x^2-48000 x+64000\right )+\text {$\#$1}^2 \left (225 x^2-1800 x+3600\right )+\text {$\#$1} (96-24 x)+1\&,1\right ]} \\
y(x)\to -\frac {x}{4}+\frac {1}{4 \text {Root}\left [\text {$\#$1}^6 \left (-3125 x^6+75000 x^5-750000 x^4+4000000 x^3-12000000 x^2+19200000 x-12800000+3125 e^{\frac {15 c_1}{8}}\right )+\text {$\#$1}^4 \left (1875 x^4-30000 x^3+180000 x^2-480000 x+480000\right )+\text {$\#$1}^3 \left (-1000 x^3+12000 x^2-48000 x+64000\right )+\text {$\#$1}^2 \left (225 x^2-1800 x+3600\right )+\text {$\#$1} (96-24 x)+1\&,2\right ]} \\
y(x)\to -\frac {x}{4}+\frac {1}{4 \text {Root}\left [\text {$\#$1}^6 \left (-3125 x^6+75000 x^5-750000 x^4+4000000 x^3-12000000 x^2+19200000 x-12800000+3125 e^{\frac {15 c_1}{8}}\right )+\text {$\#$1}^4 \left (1875 x^4-30000 x^3+180000 x^2-480000 x+480000\right )+\text {$\#$1}^3 \left (-1000 x^3+12000 x^2-48000 x+64000\right )+\text {$\#$1}^2 \left (225 x^2-1800 x+3600\right )+\text {$\#$1} (96-24 x)+1\&,3\right ]} \\
y(x)\to -\frac {x}{4}+\frac {1}{4 \text {Root}\left [\text {$\#$1}^6 \left (-3125 x^6+75000 x^5-750000 x^4+4000000 x^3-12000000 x^2+19200000 x-12800000+3125 e^{\frac {15 c_1}{8}}\right )+\text {$\#$1}^4 \left (1875 x^4-30000 x^3+180000 x^2-480000 x+480000\right )+\text {$\#$1}^3 \left (-1000 x^3+12000 x^2-48000 x+64000\right )+\text {$\#$1}^2 \left (225 x^2-1800 x+3600\right )+\text {$\#$1} (96-24 x)+1\&,4\right ]} \\
y(x)\to -\frac {x}{4}+\frac {1}{4 \text {Root}\left [\text {$\#$1}^6 \left (-3125 x^6+75000 x^5-750000 x^4+4000000 x^3-12000000 x^2+19200000 x-12800000+3125 e^{\frac {15 c_1}{8}}\right )+\text {$\#$1}^4 \left (1875 x^4-30000 x^3+180000 x^2-480000 x+480000\right )+\text {$\#$1}^3 \left (-1000 x^3+12000 x^2-48000 x+64000\right )+\text {$\#$1}^2 \left (225 x^2-1800 x+3600\right )+\text {$\#$1} (96-24 x)+1\&,5\right ]} \\
y(x)\to -\frac {x}{4}+\frac {1}{4 \text {Root}\left [\text {$\#$1}^6 \left (-3125 x^6+75000 x^5-750000 x^4+4000000 x^3-12000000 x^2+19200000 x-12800000+3125 e^{\frac {15 c_1}{8}}\right )+\text {$\#$1}^4 \left (1875 x^4-30000 x^3+180000 x^2-480000 x+480000\right )+\text {$\#$1}^3 \left (-1000 x^3+12000 x^2-48000 x+64000\right )+\text {$\#$1}^2 \left (225 x^2-1800 x+3600\right )+\text {$\#$1} (96-24 x)+1\&,6\right ]} \\
\end{align*}