60.1.263 problem 264

Internal problem ID [10277]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 264
Date solved : Monday, January 27, 2025 at 06:43:26 PM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.670 (sec). Leaf size: 37

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

\[ y = \frac {\operatorname {RootOf}\left (\textit {\_Z}^{98} c_{1} -14 \textit {\_Z}^{77} c_{1} +49 \textit {\_Z}^{56} c_{1} -9 x^{7}\right )^{21}-7}{3 x^{3}} \]

✓ Solution by Mathematica

Time used: 0.279 (sec). Leaf size: 76

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

\[ \text {Solve}\left [(-110)^{2/3} \log (x)+72 c_1=72 \int _1^{\frac {(-1)^{2/3} \left (x^3 y(x)-11\right )}{\sqrt [3]{110} \left (y(x) x^3+1\right )}}\frac {1}{K[1]^3+\frac {111 \sqrt [3]{-1} K[1]}{110^{2/3}}+1}dK[1],y(x)\right ] \]