Internal problem ID [3745]
Internal file name [OUTPUT/3238_Sunday_June_05_2022_09_02_25_AM_48308778/index.tex]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 18
Problem number: 491.
ODE order: 1.
ODE degree: 1.
The type(s) of ODE detected by this program : "unknown"
Maple gives the following as the ode type
[_rational, [_Abel, `2nd type`, `class A`]]
Unable to solve or complete the solution.
\[ \boxed {\left (x +4 x^{3}+5 y\right ) y^{\prime }+3 y x^{2}+4 y=-7 x^{3}} \] Unable to determine ODE type.
\[ \begin {array}{lll} & {} & \textrm {Let's solve}\hspace {3pt} \\ {} & {} & \left (x +4 x^{3}+5 y\right ) y^{\prime }+3 y x^{2}+4 y=-7 x^{3} \\ \bullet & {} & \textrm {Highest derivative means the order of the ODE is}\hspace {3pt} 1 \\ {} & {} & y^{\prime } \\ \bullet & {} & \textrm {Solve for the highest derivative}\hspace {3pt} \\ {} & {} & y^{\prime }=\frac {-7 x^{3}-3 y x^{2}-4 y}{x +4 x^{3}+5 y} \end {array} \]
Maple trace
`Methods for first order ODEs: --- Trying classification methods --- trying a quadrature trying 1st order linear trying Bernoulli trying separable trying inverse linear trying homogeneous types: trying Chini differential order: 1; looking for linear symmetries trying exact trying Abel <- Abel successful`
✓ Solution by Maple
Time used: 0.0 (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: 60.408 (sec). Leaf size: 3641
DSolve[(x+4 x^3+5 y[x])y'[x]+7 x^3+3 x^2 y[x]+4 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Too large to display