Internal problem ID [3400]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 23
Problem number: 661.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational]
Solve \begin {gather*} \boxed {x \left (3 x -7 y^{2}\right ) y^{\prime }+\left (5 x -3 y^{2}\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.312 (sec). Leaf size: 52
dsolve(x*(3*x-7*y(x)^2)*diff(y(x),x)+(5*x-3*y(x)^2)*y(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: 4.225 (sec). Leaf size: 288
DSolve[x(3 x-7 y[x]^2)y'[x]+(5 x-3 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*}