69.1.26 problem 43

Internal problem ID [14179]
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 : Tuesday, January 28, 2025 at 06:19:11 AM
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*}

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

DSolve[(8*y[x]+10*x)+(5*y[x]+7*x)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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