29.25.20 problem 717

Internal problem ID [5307]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 25
Problem number : 717
Date solved : Monday, January 27, 2025 at 11:08:12 AM
CAS classification : [_rational]

\begin{align*} x^{3} \left (1+5 x^{3} y^{7}\right ) y^{\prime }+\left (3 x^{5} y^{5}-1\right ) y^{3}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 25

dsolve(x^3*(1+5*x^3*y(x)^7)*diff(y(x),x)+(3*x^5*y(x)^5-1)*y(x)^3 = 0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 5.116 (sec). Leaf size: 253

DSolve[x^3(1+5 x^3 y[x]^7)D[y[x],x]+(3 x^5 y[x]^5-1)y[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
 

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