Internal problem ID [3514]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 9
Problem number: 258.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, _Riccati]
\[ \boxed {y^{\prime } x^{2}-\left (1+2 x -y\right )^{2}=0} \]
✓ Solution by Maple
Time used: 0.282 (sec). Leaf size: 24
dsolve(x^2*diff(y(x),x) = (1+2*x-y(x))^2,y(x), singsol=all)
\[ y \left (x \right ) = 1+\frac {x \left (c_{1} x^{3}-4\right )}{c_{1} x^{3}-1} \]
✓ Solution by Mathematica
Time used: 0.264 (sec). Leaf size: 41
DSolve[x^2 y'[x]==(1+2 x-y[x])^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^4+x^3+12 c_1 x+3 c_1}{x^3+3 c_1} y(x)\to 4 x+1 \end{align*}