62.10.3 problem Ex 3

Internal problem ID [12840]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter 2, differential equations of the first order and the first degree. Article 17. Other forms which Integrating factors can be found. Page 25
Problem number : Ex 3
Date solved : Tuesday, January 28, 2025 at 04:26:29 AM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} y^{4}+2 y+\left (x y^{3}+2 y^{4}-4 x \right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 27

dsolve((y(x)^4+2*y(x))+(x*y(x)^3+2*y(x)^4-4*x)*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.250 (sec). Leaf size: 129

DSolve[(y[x]^4+2*y[x])+(x*y[x]^3+2*y[x]^4-4*x)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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