29.16.6 problem 449

Internal problem ID [5047]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 16
Problem number : 449
Date solved : Monday, January 27, 2025 at 10:05:37 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (4+2 x -y\right ) y^{\prime }+5+x -2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 1.097 (sec). Leaf size: 115

dsolve((4+2*x-y(x))*diff(y(x),x)+5+x-2*y(x) = 0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 60.186 (sec). Leaf size: 1601

DSolve[(4+2 x-y[x])D[y[x],x]+5+x-2 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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