60.1.320 problem 321

Internal problem ID [10334]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 321
Date solved : Monday, January 27, 2025 at 07:13:18 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

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

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 46

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

\begin{align*} y &= -{\frac {1}{2}} \\ y &= \frac {{\mathrm e}^{\operatorname {RootOf}\left ({\mathrm e}^{3 \textit {\_Z}} x -4 x \,{\mathrm e}^{2 \textit {\_Z}}+8 c_{1} x \,{\mathrm e}^{\textit {\_Z}}+2 \textit {\_Z} x \,{\mathrm e}^{\textit {\_Z}}+3 x \,{\mathrm e}^{\textit {\_Z}}+16\right )}}{2}-\frac {1}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.174 (sec). Leaf size: 52

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

\[ \text {Solve}\left [\int _1^{y(x)}\left (-\frac {K[1]}{8}-\frac {1}{16 (2 K[1]+1)}+\frac {1}{16}\right )dK[1]-\frac {1}{4 x (2 y(x)+1)}=c_1,y(x)\right ] \]