29.17.6 problem 465

Internal problem ID [5063]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 17
Problem number : 465
Date solved : Monday, January 27, 2025 at 10:07:16 AM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.694 (sec). Leaf size: 33

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

\[ y \left (x \right ) = \frac {-\sqrt {4-27 \left (x +\frac {1}{3}\right )^{2} c_{1}^{2}}+\left (3 x +3\right ) c_{1}}{6 c_{1}} \]

✓ Solution by Mathematica

Time used: 0.132 (sec). Leaf size: 67

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

\begin{align*} y(x)\to \frac {1}{2} \left (-i \sqrt {3 x^2+2 x-1-4 c_1}+x+1\right ) \\ y(x)\to \frac {1}{2} \left (i \sqrt {3 x^2+2 x-1-4 c_1}+x+1\right ) \\ \end{align*}