29.18.9 problem 485

Internal problem ID [5083]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 18
Problem number : 485
Date solved : Monday, January 27, 2025 at 10:08:31 AM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (5+2 x -4 y\right ) y^{\prime }&=3+x -2 y \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 41

dsolve((5+2*x-4*y(x))*diff(y(x),x) = 3+x-2*y(x),y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \frac {x}{2}+\frac {5}{4}-\frac {\sqrt {4 c_{1} -4 x +25}}{4} \\ y \left (x \right ) &= \frac {x}{2}+\frac {5}{4}+\frac {\sqrt {4 c_{1} -4 x +25}}{4} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.118 (sec). Leaf size: 61

DSolve[(5+2 x-4 y[x])D[y[x],x]==3+x-2 y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{4} \left (2 x-i \sqrt {4 x-25-16 c_1}+5\right ) \\ y(x)\to \frac {1}{4} \left (2 x+i \sqrt {4 x-25-16 c_1}+5\right ) \\ \end{align*}