22.22 problem 630

Internal problem ID [3878]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 22
Problem number: 630.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, `class C`], _rational]

\[ \boxed {\left (1-3 x +2 y\right )^{2} y^{\prime }-\left (4+2 x -3 y\right )^{2}=0} \]

Solution by Maple

Time used: 1.453 (sec). Leaf size: 309

dsolve((1-3*x+2*y(x))^2*diff(y(x),x) = (4+2*x-3*y(x))^2,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {14}{5}+\frac {\left (-11+5 x \right ) \left (\operatorname {RootOf}\left (59049 \left (-11+5 x \right )^{9} c_{1} \textit {\_Z}^{90}+\left (-295245 \left (-11+5 x \right )^{9} c_{1} +1\right ) \textit {\_Z}^{81}+459270 \left (-11+5 x \right )^{9} c_{1} \textit {\_Z}^{72}-65610 \left (-11+5 x \right )^{9} c_{1} \textit {\_Z}^{63}-375435 \left (-11+5 x \right )^{9} c_{1} \textit {\_Z}^{54}+115911 \left (-11+5 x \right )^{9} c_{1} \textit {\_Z}^{45}+166860 \left (-11+5 x \right )^{9} c_{1} \textit {\_Z}^{36}-12960 \left (-11+5 x \right )^{9} c_{1} \textit {\_Z}^{27}-40320 \left (-11+5 x \right )^{9} c_{1} \textit {\_Z}^{18}-11520 \left (-11+5 x \right )^{9} c_{1} \textit {\_Z}^{9}-1024 \left (-11+5 x \right )^{9} c_{1} \right )^{9}-1\right )}{5 \operatorname {RootOf}\left (59049 \left (-11+5 x \right )^{9} c_{1} \textit {\_Z}^{90}+\left (-295245 \left (-11+5 x \right )^{9} c_{1} +1\right ) \textit {\_Z}^{81}+459270 \left (-11+5 x \right )^{9} c_{1} \textit {\_Z}^{72}-65610 \left (-11+5 x \right )^{9} c_{1} \textit {\_Z}^{63}-375435 \left (-11+5 x \right )^{9} c_{1} \textit {\_Z}^{54}+115911 \left (-11+5 x \right )^{9} c_{1} \textit {\_Z}^{45}+166860 \left (-11+5 x \right )^{9} c_{1} \textit {\_Z}^{36}-12960 \left (-11+5 x \right )^{9} c_{1} \textit {\_Z}^{27}-40320 \left (-11+5 x \right )^{9} c_{1} \textit {\_Z}^{18}-11520 \left (-11+5 x \right )^{9} c_{1} \textit {\_Z}^{9}-1024 \left (-11+5 x \right )^{9} c_{1} \right )^{9}} \]

Solution by Mathematica

Time used: 60.209 (sec). Leaf size: 3501

DSolve[(1-3 x+2 y[x])^2 y'[x]==(4+2 x-3 y[x])^2,y[x],x,IncludeSingularSolutions -> True]
 

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