29.16.11 problem 454

Internal problem ID [5052]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 16
Problem number : 454
Date solved : Monday, January 27, 2025 at 10:06:05 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (6-4 x -y\right ) y^{\prime }&=2 x -y \end{align*}

✓ Solution by Maple

Time used: 0.150 (sec). Leaf size: 196

dsolve((6-4*x-y(x))*diff(y(x),x) = 2*x-y(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\frac {\left (1-i \sqrt {3}\right ) \left (12 \sqrt {3}\, c_{1}^{2} \left (x -1\right ) \sqrt {\frac {27 \left (x -1\right )^{2} c_{1} -4 x +4}{c_{1}}}+8+108 \left (x -1\right )^{2} c_{1}^{2}+\left (-72 x +72\right ) c_{1} \right )^{{2}/{3}}}{12}-\left (\frac {1}{3}+c_{1} \left (x -3\right )\right ) \left (12 \sqrt {3}\, c_{1}^{2} \left (x -1\right ) \sqrt {\frac {27 \left (x -1\right )^{2} c_{1} -4 x +4}{c_{1}}}+8+108 \left (x -1\right )^{2} c_{1}^{2}+\left (-72 x +72\right ) c_{1} \right )^{{1}/{3}}+2 \left (-1-i \sqrt {3}\right ) \left (-\frac {1}{6}+c_{1} \left (x -1\right )\right )}{\left (12 \sqrt {3}\, c_{1}^{2} \left (x -1\right ) \sqrt {\frac {27 \left (x -1\right )^{2} c_{1} -4 x +4}{c_{1}}}+8+108 \left (x -1\right )^{2} c_{1}^{2}+\left (-72 x +72\right ) c_{1} \right )^{{1}/{3}} c_{1}} \]

✓ Solution by Mathematica

Time used: 60.100 (sec). Leaf size: 2581

DSolve[(6-4 x-y[x])D[y[x],x]==2 x -y[x],y[x],x,IncludeSingularSolutions -> True]
 

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