29.9.18 problem 258

Internal problem ID [4858]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 9
Problem number : 258
Date solved : Monday, January 27, 2025 at 09:42:56 AM
CAS classification : [[_homogeneous, `class C`], _rational, _Riccati]

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

✓ Solution by Maple

Time used: 1.117 (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: 0.283 (sec). Leaf size: 41

DSolve[x^2 D[y[x],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*}