29.17.10 problem 469

Internal problem ID [5067]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 17
Problem number : 469
Date solved : Monday, January 27, 2025 at 10:07:29 AM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (3+2 x -2 y\right ) y^{\prime }&=1+6 x -2 y \end{align*}

✓ Solution by Maple

Time used: 0.696 (sec). Leaf size: 33

dsolve((3+2*x-2*y(x))*diff(y(x),x) = 1+6*x-2*y(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {-\sqrt {1-8 \left (x -\frac {1}{2}\right )^{2} c_{1}^{2}}+\left (3+2 x \right ) c_{1}}{2 c_{1}} \]

✓ Solution by Mathematica

Time used: 0.136 (sec). Leaf size: 67

DSolve[(3+2 x-2 y[x])D[y[x],x]==1+6 x-2 y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{2} i \sqrt {8 x^2-8 x-9-4 c_1}+x+\frac {3}{2} \\ y(x)\to \frac {1}{2} i \sqrt {8 x^2-8 x-9-4 c_1}+x+\frac {3}{2} \\ \end{align*}