Internal problem ID [10172]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational]
Solve \begin {gather*} \boxed {5 y x -3 y^{3}+\left (3 x^{2}-7 y^{2} x \right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.578 (sec). Leaf size: 52
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 \relax (x ) = \RootOf \left (x \,\textit {\_Z}^{7}-x^{2} \textit {\_Z}^{3}-\frac {c_{1}}{\sqrt {x}}\right )^{2} \\ y \relax (x ) = \RootOf \left (x \,\textit {\_Z}^{7}-x^{2} \textit {\_Z}^{3}+\frac {c_{1}}{\sqrt {x}}\right )^{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 4.565 (sec). Leaf size: 288
DSolve[(5*x*y[x]-3*y[x]^3)+(3*x^2-7*x*y[x]^2)*y'[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*}