63.1.26 problem 43
Internal
problem
ID
[15466]
Book
:
DIFFERENTIAL
and
INTEGRAL
CALCULUS.
VOL
I.
by
N.
PISKUNOV.
MIR
PUBLISHERS,
Moscow
1969.
Section
:
Chapter
8.
Differential
equations.
Exercises
page
595
Problem
number
:
43
Date
solved
:
Thursday, October 02, 2025 at 10:15:32 AM
CAS
classification
:
[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]
\begin{align*} \left (7 x +5 y\right ) y^{\prime }+10 x +8 y&=0 \end{align*}
✓ Maple. Time used: 0.034 (sec). Leaf size: 283
ode:=8*y(x)+10*x+(5*y(x)+7*x)*diff(y(x),x) = 0;
dsolve(ode,y(x), singsol=all);
\[
y = \frac {x \left ({\mathrm e}^{-\frac {5 c_1}{2}}-\sqrt {x^{2} \operatorname {RootOf}\left (\textit {\_Z}^{5} x^{2} {\mathrm e}^{2 c_1} \operatorname {RootOf}\left (\textit {\_Z}^{2}-x \,{\mathrm e}^{c_1}, \operatorname {index} =1\right )-\textit {\_Z}^{3} x^{2} {\mathrm e}^{2 c_1} \operatorname {RootOf}\left (\textit {\_Z}^{2}-x \,{\mathrm e}^{c_1}, \operatorname {index} =1\right )-1\right ) \left (\operatorname {RootOf}\left (\textit {\_Z}^{5} x^{2} {\mathrm e}^{2 c_1} \operatorname {RootOf}\left (\textit {\_Z}^{2}-x \,{\mathrm e}^{c_1}, \operatorname {index} =1\right )-\textit {\_Z}^{3} x^{2} {\mathrm e}^{2 c_1} \operatorname {RootOf}\left (\textit {\_Z}^{2}-x \,{\mathrm e}^{c_1}, \operatorname {index} =1\right )-1\right )^{3} x^{3}+{\mathrm e}^{-3 c_1} \operatorname {RootOf}\left (\textit {\_Z}^{2}-x \,{\mathrm e}^{c_1}, \operatorname {index} =1\right )\right )}\right )}{\sqrt {x^{2} \operatorname {RootOf}\left (\textit {\_Z}^{5} x^{2} {\mathrm e}^{2 c_1} \operatorname {RootOf}\left (\textit {\_Z}^{2}-x \,{\mathrm e}^{c_1}, \operatorname {index} =1\right )-\textit {\_Z}^{3} x^{2} {\mathrm e}^{2 c_1} \operatorname {RootOf}\left (\textit {\_Z}^{2}-x \,{\mathrm e}^{c_1}, \operatorname {index} =1\right )-1\right ) \left (\operatorname {RootOf}\left (\textit {\_Z}^{5} x^{2} {\mathrm e}^{2 c_1} \operatorname {RootOf}\left (\textit {\_Z}^{2}-x \,{\mathrm e}^{c_1}, \operatorname {index} =1\right )-\textit {\_Z}^{3} x^{2} {\mathrm e}^{2 c_1} \operatorname {RootOf}\left (\textit {\_Z}^{2}-x \,{\mathrm e}^{c_1}, \operatorname {index} =1\right )-1\right )^{3} x^{3}+{\mathrm e}^{-3 c_1} \operatorname {RootOf}\left (\textit {\_Z}^{2}-x \,{\mathrm e}^{c_1}, \operatorname {index} =1\right )\right )}}
\]
✓ Mathematica. Time used: 2.544 (sec). Leaf size: 276
ode=(8*y[x]+10*x)+(5*y[x]+7*x)*D[y[x],x]==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*} y(x)&\to \text {Root}\left [\text {$\#$1}^5+8 \text {$\#$1}^4 x+25 \text {$\#$1}^3 x^2+38 \text {$\#$1}^2 x^3+28 \text {$\#$1} x^4+8 x^5-e^{c_1}\&,1\right ]\\ y(x)&\to \text {Root}\left [\text {$\#$1}^5+8 \text {$\#$1}^4 x+25 \text {$\#$1}^3 x^2+38 \text {$\#$1}^2 x^3+28 \text {$\#$1} x^4+8 x^5-e^{c_1}\&,2\right ]\\ y(x)&\to \text {Root}\left [\text {$\#$1}^5+8 \text {$\#$1}^4 x+25 \text {$\#$1}^3 x^2+38 \text {$\#$1}^2 x^3+28 \text {$\#$1} x^4+8 x^5-e^{c_1}\&,3\right ]\\ y(x)&\to \text {Root}\left [\text {$\#$1}^5+8 \text {$\#$1}^4 x+25 \text {$\#$1}^3 x^2+38 \text {$\#$1}^2 x^3+28 \text {$\#$1} x^4+8 x^5-e^{c_1}\&,4\right ]\\ y(x)&\to \text {Root}\left [\text {$\#$1}^5+8 \text {$\#$1}^4 x+25 \text {$\#$1}^3 x^2+38 \text {$\#$1}^2 x^3+28 \text {$\#$1} x^4+8 x^5-e^{c_1}\&,5\right ] \end{align*}
✓ Sympy. Time used: 0.465 (sec). Leaf size: 26
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(10*x + (7*x + 5*y(x))*Derivative(y(x), x) + 8*y(x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\log {\left (x \right )} = C_{1} - \log {\left (\left (1 + \frac {y{\left (x \right )}}{x}\right )^{\frac {2}{5}} \left (2 + \frac {y{\left (x \right )}}{x}\right )^{\frac {3}{5}} \right )}
\]