60.1.261 problem 262

Internal problem ID [10275]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 262
Date solved : Monday, January 27, 2025 at 06:42:58 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class C`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.550 (sec). Leaf size: 65

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

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

✓ Solution by Mathematica

Time used: 0.123 (sec). Leaf size: 48

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

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