29.16.8 problem 451

Internal problem ID [5049]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 16
Problem number : 451
Date solved : Monday, January 27, 2025 at 10:05:46 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 1.678 (sec). Leaf size: 45

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

\[ y \left (x \right ) = \frac {1}{2}-\frac {\left (2 x -1\right ) \left (1+\operatorname {RootOf}\left (-3+\left (8 c_{1} x^{3}-12 c_{1} x^{2}+6 c_{1} x -c_{1} \right ) \textit {\_Z}^{4}-\textit {\_Z} \right )\right )}{2} \]

✓ Solution by Mathematica

Time used: 60.165 (sec). Leaf size: 4937

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

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