Internal problem ID [3006]
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]
Solve \begin {gather*} \boxed {y^{\prime } x^{2}-\left (1+2 x -y\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.242 (sec). Leaf size: 24
dsolve(x^2*diff(y(x),x) = (1+2*x-y(x))^2,y(x), singsol=all)
\[ y \relax (x ) = 1+\frac {x \left (c_{1} x^{3}-4\right )}{c_{1} x^{3}-1} \]
✓ Solution by Mathematica
Time used: 0.24 (sec). Leaf size: 34
DSolve[x^2 y'[x]==(1+2 x-y[x])^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {3 x^4}{x^3+3 c_1}+4 x+1 \\ y(x)\to 4 x+1 \\ \end{align*}