60.1.184 problem 185

Internal problem ID [10198]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 185
Date solved : Tuesday, January 28, 2025 at 04:26:32 PM
CAS classification : [_rational, _Abel]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 78

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

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

✓ Solution by Mathematica

Time used: 0.333 (sec). Leaf size: 123

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

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