60.1.318 problem 319

Internal problem ID [10332]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 319
Date solved : Monday, January 27, 2025 at 07:13:14 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} \left (7 x y^{3}+y-5 x \right ) y^{\prime }+y^{4}-5 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 34

dsolve((7*x*y(x)^3+y(x)-5*x)*diff(y(x),x)+y(x)^4-5*y(x) = 0,y(x), singsol=all)
 

\[ x +\frac {\frac {y^{5}}{5}-\frac {5 y^{2}}{2}-c_{1}}{y \left (y^{3}-5\right )^{2}} = 0 \]

✓ Solution by Mathematica

Time used: 5.205 (sec). Leaf size: 132

DSolve[-5*y[x] + y[x]^4 + (-5*x + y[x] + 7*x*y[x]^3)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [x=\exp \left (\int _1^{y(x)}\frac {7 K[1]^3-5}{5 K[1]-K[1]^4}dK[1]\right ) \int _1^{y(x)}\frac {\exp \left (-\int _1^{K[2]}\frac {7 K[1]^3-5}{5 K[1]-K[1]^4}dK[1]\right ) K[2]}{5 K[2]-K[2]^4}dK[2]+c_1 \exp \left (\int _1^{y(x)}\frac {7 K[1]^3-5}{5 K[1]-K[1]^4}dK[1]\right ),y(x)\right ] \]