29.14.1 problem 380

Internal problem ID [4980]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 14
Problem number : 380
Date solved : Tuesday, January 28, 2025 at 02:41:20 PM
CAS classification : [_rational, _Abel]

\begin{align*} x^{7} y^{\prime }+5 x^{3} y^{2}+2 \left (x^{2}+1\right ) y^{3}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 78

dsolve(x^7*diff(y(x),x)+5*x^3*y(x)^2+2*(x^2+1)*y(x)^3 = 0,y(x), singsol=all)
 

\[ c_{1} +\frac {x}{\left (\frac {x^{6}+x^{2} y \left (x \right )^{2}+2 x^{3} y \left (x \right )+y \left (x \right )^{2}}{x^{2} y \left (x \right )^{2}}\right )^{{1}/{4}}}+\frac {\left (x^{3}+y \left (x \right )\right ) \operatorname {hypergeom}\left (\left [\frac {1}{2}, \frac {5}{4}\right ], \left [\frac {3}{2}\right ], -\frac {\left (x^{3}+y \left (x \right )\right )^{2}}{x^{2} y \left (x \right )^{2}}\right )}{2 x y \left (x \right )} = 0 \]

✓ Solution by Mathematica

Time used: 0.317 (sec). Leaf size: 123

DSolve[x^7 D[y[x],x]+5 x^3 y[x]^2+2(1+x^2)y[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [c_1=\frac {\frac {1}{2} \sqrt [4]{1-\left (\frac {i x^2}{y(x)}+\frac {i}{x}\right )^2} \left (\frac {i x^2}{y(x)}+\frac {i}{x}\right ) \operatorname {Hypergeometric2F1}\left (\frac {1}{2},\frac {5}{4},\frac {3}{2},\left (\frac {i x^2}{y(x)}+\frac {i}{x}\right )^2\right )+i x}{\sqrt [4]{-1+\left (\frac {i x^2}{y(x)}+\frac {i}{x}\right )^2}},y(x)\right ] \]