18.21 problem 497

Internal problem ID [3243]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 18
Problem number: 497.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]]

Solve \begin {gather*} \boxed {\left (140+7 x -16 y\right ) y^{\prime }+25+8 x +y=0} \end {gather*}

Solution by Maple

Time used: 0.203 (sec). Leaf size: 332

dsolve((140+7*x-16*y(x))*diff(y(x),x)+25+8*x+y(x) = 0,y(x), singsol=all)
 

\[ y \relax (x ) = 7+\frac {\left (4+x \right )^{8} \RootOf \left (\left (4+x \right )^{8} c_{1} \textit {\_Z}^{64}+9 \left (4+x \right )^{8} c_{1} \textit {\_Z}^{56}+27 \left (4+x \right )^{8} c_{1} \textit {\_Z}^{48}+27 \left (4+x \right )^{8} c_{1} \textit {\_Z}^{40}-8\right )^{56}+6 \left (4+x \right )^{8} \RootOf \left (\left (4+x \right )^{8} c_{1} \textit {\_Z}^{64}+9 \left (4+x \right )^{8} c_{1} \textit {\_Z}^{56}+27 \left (4+x \right )^{8} c_{1} \textit {\_Z}^{48}+27 \left (4+x \right )^{8} c_{1} \textit {\_Z}^{40}-8\right )^{48}+9 \left (4+x \right )^{8} \RootOf \left (\left (4+x \right )^{8} c_{1} \textit {\_Z}^{64}+9 \left (4+x \right )^{8} c_{1} \textit {\_Z}^{56}+27 \left (4+x \right )^{8} c_{1} \textit {\_Z}^{48}+27 \left (4+x \right )^{8} c_{1} \textit {\_Z}^{40}-8\right )^{40}-\frac {4}{c_{1}}}{\left (4+x \right )^{7} \RootOf \left (\left (4+x \right )^{8} c_{1} \textit {\_Z}^{64}+9 \left (4+x \right )^{8} c_{1} \textit {\_Z}^{56}+27 \left (4+x \right )^{8} c_{1} \textit {\_Z}^{48}+27 \left (4+x \right )^{8} c_{1} \textit {\_Z}^{40}-8\right )^{40} \left (\RootOf \left (\left (4+x \right )^{8} c_{1} \textit {\_Z}^{64}+9 \left (4+x \right )^{8} c_{1} \textit {\_Z}^{56}+27 \left (4+x \right )^{8} c_{1} \textit {\_Z}^{48}+27 \left (4+x \right )^{8} c_{1} \textit {\_Z}^{40}-8\right )^{16}+6 \RootOf \left (\left (4+x \right )^{8} c_{1} \textit {\_Z}^{64}+9 \left (4+x \right )^{8} c_{1} \textit {\_Z}^{56}+27 \left (4+x \right )^{8} c_{1} \textit {\_Z}^{48}+27 \left (4+x \right )^{8} c_{1} \textit {\_Z}^{40}-8\right )^{8}+9\right )} \]

Solution by Mathematica

Time used: 60.06 (sec). Leaf size: 1673

DSolve[(140+7 x-16 y[x])y'[x]+25+8 x+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

Too large to display