29.18.15 problem 491

Internal problem ID [5089]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 18
Problem number : 491
Date solved : Tuesday, January 28, 2025 at 02:41:26 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (x +4 x^{3}+5 y\right ) y^{\prime }+7 x^{3}+3 x^{2} y+4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 588

dsolve((x+4*x^3+5*y(x))*diff(y(x),x)+7*x^3+3*x^2*y(x)+4*y(x) = 0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {16 \left (-x^{15}+5 x^{13}-10 x^{11}+10 x^{9}-5 x^{7}+x^{5}+48 c_{1} \right ) {\operatorname {RootOf}\left (\left (-2 x^{15}+10 x^{13}-20 x^{11}+20 x^{9}-10 x^{7}+2 x^{5}+96 c_{1} \right ) \textit {\_Z}^{25}+\left (-35 x^{15}+175 x^{13}-350 x^{11}+350 x^{9}-175 x^{7}+35 x^{5}+1680 c_{1} \right ) \textit {\_Z}^{20}+11760 c_{1} \textit {\_Z}^{15}+41160 c_{1} \textit {\_Z}^{10}+72030 c_{1} \textit {\_Z}^{5}+50421 c_{1} \right )}^{20}+224 \left (-x^{15}+5 x^{13}-10 x^{11}+10 x^{9}-5 x^{7}+x^{5}+48 c_{1} \right ) {\operatorname {RootOf}\left (\left (-2 x^{15}+10 x^{13}-20 x^{11}+20 x^{9}-10 x^{7}+2 x^{5}+96 c_{1} \right ) \textit {\_Z}^{25}+\left (-35 x^{15}+175 x^{13}-350 x^{11}+350 x^{9}-175 x^{7}+35 x^{5}+1680 c_{1} \right ) \textit {\_Z}^{20}+11760 c_{1} \textit {\_Z}^{15}+41160 c_{1} \textit {\_Z}^{10}+72030 c_{1} \textit {\_Z}^{5}+50421 c_{1} \right )}^{15}+784 \left (x^{15}-5 x^{13}+10 x^{11}-10 x^{9}+5 x^{7}-x^{5}+72 c_{1} \right ) {\operatorname {RootOf}\left (\left (-2 x^{15}+10 x^{13}-20 x^{11}+20 x^{9}-10 x^{7}+2 x^{5}+96 c_{1} \right ) \textit {\_Z}^{25}+\left (-35 x^{15}+175 x^{13}-350 x^{11}+350 x^{9}-175 x^{7}+35 x^{5}+1680 c_{1} \right ) \textit {\_Z}^{20}+11760 c_{1} \textit {\_Z}^{15}+41160 c_{1} \textit {\_Z}^{10}+72030 c_{1} \textit {\_Z}^{5}+50421 c_{1} \right )}^{10}+2744 \left (-x^{15}+5 x^{13}-10 x^{11}+10 x^{9}-5 x^{7}+x^{5}+48 c_{1} \right ) {\operatorname {RootOf}\left (\left (-2 x^{15}+10 x^{13}-20 x^{11}+20 x^{9}-10 x^{7}+2 x^{5}+96 c_{1} \right ) \textit {\_Z}^{25}+\left (-35 x^{15}+175 x^{13}-350 x^{11}+350 x^{9}-175 x^{7}+35 x^{5}+1680 c_{1} \right ) \textit {\_Z}^{20}+11760 c_{1} \textit {\_Z}^{15}+41160 c_{1} \textit {\_Z}^{10}+72030 c_{1} \textit {\_Z}^{5}+50421 c_{1} \right )}^{5}-12005 x^{13}+48020 x^{11}-72030 x^{9}+48020 x^{7}-12005 x^{5}+115248 c_{1}}{12005 x^{4} \left (x -1\right )^{4} \left (x +1\right )^{4}} \]

✓ Solution by Mathematica

Time used: 60.270 (sec). Leaf size: 9701

DSolve[(x+4 x^3+5 y[x])D[y[x],x]+7 x^3+3 x^2 y[x]+4 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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