60.1.244 problem 245

Internal problem ID [10258]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 245
Date solved : Monday, January 27, 2025 at 06:42:02 PM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} \left (2 y x +4 x^{3}\right ) y^{\prime }+y^{2}+112 x^{2} y&=0 \end{align*}

✓ Solution by Maple

Time used: 3.056 (sec). Leaf size: 31

dsolve((2*x*y(x)+4*x^3)*diff(y(x),x)+y(x)^2+112*x^2*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{1}}{x^{28} \operatorname {RootOf}\left (x^{30} \textit {\_Z}^{360}-24 x^{30} \textit {\_Z}^{330}-c_{1} \right )^{330}} \]

✓ Solution by Mathematica

Time used: 0.372 (sec). Leaf size: 97

DSolve[(2*x*y[x]+4*x^3)*D[y[x],x]+y[x]^2+112*x^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{\frac {2^{2/3} \left (5 x^2 y(x)-23 x^4\right )}{\sqrt [3]{1495} \sqrt [3]{x^6} \left (2 x^2+y(x)\right )}}\frac {1}{K[1]^3-\frac {399 K[1]}{2990^{2/3}}+1}dK[1]+\frac {5\ 1495^{2/3} \left (x^6\right )^{2/3} \log (x)}{99 \sqrt [3]{2} x^4}=c_1,y(x)\right ] \]