Internal problem ID [8622]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 286.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational]
\[ \boxed {\left (2 y-3 x +1\right )^{2} y^{\prime }-\left (3 y-2 x -4\right )^{2}=0} \]
✓ Solution by Maple
Time used: 1.438 (sec). Leaf size: 309
dsolve((2*y(x)-3*x+1)^2*diff(y(x),x)-(3*y(x)-2*x-4)^2=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {14}{5}+\frac {\left (5 x -11\right ) \left (\operatorname {RootOf}\left (59049 \left (5 x -11\right )^{9} c_{1} \textit {\_Z}^{90}+\left (-295245 \left (5 x -11\right )^{9} c_{1} +1\right ) \textit {\_Z}^{81}+459270 \left (5 x -11\right )^{9} c_{1} \textit {\_Z}^{72}-65610 \left (5 x -11\right )^{9} c_{1} \textit {\_Z}^{63}-375435 \left (5 x -11\right )^{9} c_{1} \textit {\_Z}^{54}+115911 \left (5 x -11\right )^{9} c_{1} \textit {\_Z}^{45}+166860 \left (5 x -11\right )^{9} c_{1} \textit {\_Z}^{36}-12960 \left (5 x -11\right )^{9} c_{1} \textit {\_Z}^{27}-40320 \left (5 x -11\right )^{9} c_{1} \textit {\_Z}^{18}-11520 \left (5 x -11\right )^{9} c_{1} \textit {\_Z}^{9}-1024 \left (5 x -11\right )^{9} c_{1} \right )^{9}-1\right )}{5 \operatorname {RootOf}\left (59049 \left (5 x -11\right )^{9} c_{1} \textit {\_Z}^{90}+\left (-295245 \left (5 x -11\right )^{9} c_{1} +1\right ) \textit {\_Z}^{81}+459270 \left (5 x -11\right )^{9} c_{1} \textit {\_Z}^{72}-65610 \left (5 x -11\right )^{9} c_{1} \textit {\_Z}^{63}-375435 \left (5 x -11\right )^{9} c_{1} \textit {\_Z}^{54}+115911 \left (5 x -11\right )^{9} c_{1} \textit {\_Z}^{45}+166860 \left (5 x -11\right )^{9} c_{1} \textit {\_Z}^{36}-12960 \left (5 x -11\right )^{9} c_{1} \textit {\_Z}^{27}-40320 \left (5 x -11\right )^{9} c_{1} \textit {\_Z}^{18}-11520 \left (5 x -11\right )^{9} c_{1} \textit {\_Z}^{9}-1024 \left (5 x -11\right )^{9} c_{1} \right )^{9}} \]
✓ Solution by Mathematica
Time used: 60.198 (sec). Leaf size: 3501
DSolve[(2*y[x]-3*x+1)^2*y'[x]-(3*y[x]-2*x-4)^2==0,y[x],x,IncludeSingularSolutions -> True]
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