60.1.171 problem 172

Internal problem ID [10185]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 172
Date solved : Monday, January 27, 2025 at 06:34:17 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Riccati]

\begin{align*} x^{3} y^{\prime }-x^{4} y^{2}+x^{2} y+20&=0 \end{align*}

✓ Solution by Maple

Time used: 0.490 (sec). Leaf size: 26

dsolve(x^3*diff(y(x),x) - x^4*y(x)^2 + x^2*y(x) + 20=0,y(x), singsol=all)
 

\[ y = \frac {5 x^{9}+4 c_{1}}{\left (-x^{9}+c_{1} \right ) x^{2}} \]

✓ Solution by Mathematica

Time used: 0.165 (sec). Leaf size: 36

DSolve[x^3*D[y[x],x] - x^4*y[x]^2 + x^2*y[x] + 20==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {-5 x^9+4 c_1}{x^2 \left (x^9+c_1\right )} \\ y(x)\to \frac {4}{x^2} \\ \end{align*}