62.12.16 problem Ex 17

Internal problem ID [12862]
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 19. Summary. Page 29
Problem number : Ex 17
Date solved : Tuesday, January 28, 2025 at 04:28:56 AM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} 5 y x -3 y^{3}+\left (3 x^{2}-7 x y^{2}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 15.520 (sec). Leaf size: 49

dsolve((5*x*y(x)-3*y(x)^3)+(3*x^2-7*x*y(x)^2)*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= \operatorname {RootOf}\left (x^{{3}/{2}} \textit {\_Z}^{7}-x^{{5}/{2}} \textit {\_Z}^{3}-c_{1} \right )^{2} \\ y &= \operatorname {RootOf}\left (x^{{3}/{2}} \textit {\_Z}^{7}-x^{{5}/{2}} \textit {\_Z}^{3}+c_{1} \right )^{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 4.798 (sec). Leaf size: 288

DSolve[(5*x*y[x]-3*y[x]^3)+(3*x^2-7*x*y[x]^2)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {Root}\left [4 \text {$\#$1}^7 x^3-8 \text {$\#$1}^5 x^4+4 \text {$\#$1}^3 x^5-c_1{}^2\&,1\right ] \\ y(x)\to \text {Root}\left [4 \text {$\#$1}^7 x^3-8 \text {$\#$1}^5 x^4+4 \text {$\#$1}^3 x^5-c_1{}^2\&,2\right ] \\ y(x)\to \text {Root}\left [4 \text {$\#$1}^7 x^3-8 \text {$\#$1}^5 x^4+4 \text {$\#$1}^3 x^5-c_1{}^2\&,3\right ] \\ y(x)\to \text {Root}\left [4 \text {$\#$1}^7 x^3-8 \text {$\#$1}^5 x^4+4 \text {$\#$1}^3 x^5-c_1{}^2\&,4\right ] \\ y(x)\to \text {Root}\left [4 \text {$\#$1}^7 x^3-8 \text {$\#$1}^5 x^4+4 \text {$\#$1}^3 x^5-c_1{}^2\&,5\right ] \\ y(x)\to \text {Root}\left [4 \text {$\#$1}^7 x^3-8 \text {$\#$1}^5 x^4+4 \text {$\#$1}^3 x^5-c_1{}^2\&,6\right ] \\ y(x)\to \text {Root}\left [4 \text {$\#$1}^7 x^3-8 \text {$\#$1}^5 x^4+4 \text {$\#$1}^3 x^5-c_1{}^2\&,7\right ] \\ \end{align*}