29.17.8 problem 467

Internal problem ID [5065]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 17
Problem number : 467
Date solved : Monday, January 27, 2025 at 10:07:23 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (1+x +2 y\right ) y^{\prime }+7+x -4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.149 (sec). Leaf size: 196

dsolve((1+x+2*y(x))*diff(y(x),x)+7+x-4*y(x) = 0,y(x), singsol=all)
 

\[ y \left (x \right ) = -\frac {4 \left (\left (\frac {i \sqrt {3}}{48}-\frac {1}{48}\right ) \left (12 \sqrt {3}\, c_{1}^{2} \left (x +3\right ) \sqrt {\frac {27 \left (x +3\right )^{2} c_{1} -32 x -96}{c_{1}}}+512+108 \left (x +3\right )^{2} c_{1}^{2}+\left (-576 x -1728\right ) c_{1} \right )^{{2}/{3}}+\left (\frac {1}{3}+\left (-\frac {x}{4}-1\right ) c_{1} \right ) \left (12 \sqrt {3}\, c_{1}^{2} \left (x +3\right ) \sqrt {\frac {27 \left (x +3\right )^{2} c_{1} -32 x -96}{c_{1}}}+512+108 \left (x +3\right )^{2} c_{1}^{2}+\left (-576 x -1728\right ) c_{1} \right )^{{1}/{3}}+\left (1+i \sqrt {3}\right ) \left (-\frac {4}{3}+\left (x +3\right ) c_{1} \right )\right )}{\left (12 \sqrt {3}\, c_{1}^{2} \left (x +3\right ) \sqrt {\frac {27 \left (x +3\right )^{2} c_{1} -32 x -96}{c_{1}}}+512+108 \left (x +3\right )^{2} c_{1}^{2}+\left (-576 x -1728\right ) c_{1} \right )^{{1}/{3}} c_{1}} \]

✓ Solution by Mathematica

Time used: 60.102 (sec). Leaf size: 2617

DSolve[(1+x+2 y[x])D[y[x],x]+7+x-4 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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