7.1 problem 176

Internal problem ID [2924]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 7
Problem number: 176.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, class D], _rational, _Riccati]

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

Solution by Maple

Time used: 0.002 (sec). Leaf size: 24

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

\[ y \relax (x ) = -\frac {x \left (x^{2}+2 c_{1}+2\right )}{x^{2}+2 c_{1}} \]

Solution by Mathematica

Time used: 0.154 (sec). Leaf size: 28

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

\begin{align*} y(x)\to x \left (-1-\frac {2}{x^2+2 c_1}\right ) \\ y(x)\to -x \\ \end{align*}