60.1.296 problem 297

Internal problem ID [10310]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 297
Date solved : Monday, January 27, 2025 at 07:07:36 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.624 (sec). Leaf size: 29

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

\[ y = \operatorname {RootOf}\left (\textit {\_Z}^{45} c_{1} x^{9}-\textit {\_Z}^{18}-6 \textit {\_Z}^{9}-9\right )^{{9}/{2}} x \]

✓ Solution by Mathematica

Time used: 0.122 (sec). Leaf size: 44

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

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {K[1]^2+5}{K[1] \left (K[1]^2+3\right )}dK[1]=-\frac {3 \log (x)}{2}+c_1,y(x)\right ] \]