69.1.26 problem 43

Internal problem ID [14100]
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 : Wednesday, March 05, 2025 at 10:32:57 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 8 y+10 x +\left (5 y+7 x \right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 1.480 (sec). Leaf size: 38

ode:=8*y(x)+10*x+(5*y(x)+7*x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x \left (-2+\operatorname {RootOf}\left (\textit {\_Z}^{25} c_{1} x^{5}-2 \textit {\_Z}^{20} c_{1} x^{5}+\textit {\_Z}^{15} c_{1} x^{5}-1\right )^{5}\right ) \]

✓ Mathematica. Time used: 0.038 (sec). Leaf size: 42

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]
 

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {5 K[1]+7}{(K[1]+1) (K[1]+2)}dK[1]=-5 \log (x)+c_1,y(x)\right ] \]

✓ Sympy. Time used: 0.730 (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)
 

\[ \log {\left (x \right )} = C_{1} - \log {\left (\left (1 + \frac {y{\left (x \right )}}{x}\right )^{\frac {2}{5}} \left (2 + \frac {y{\left (x \right )}}{x}\right )^{\frac {3}{5}} \right )} \]