Internal problem ID [7866]
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]
Solve \begin {gather*} \boxed {\left (1-3 x +2 y\right )^{2} y^{\prime }-\left (-4-2 x +3 y\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 1.696 (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)
\[ y \relax (x ) = \frac {14}{5}+\frac {\left (5 x -11\right ) \left (\RootOf \left (59049 \left (5 x -11\right )^{9} c_{1} \textit {\_Z}^{90}+\left (-295245 \left (5 x -11\right )^{9} c_{1}+1\right ) \textit {\_Z}^{81}+459270 \left (5 x -11\right )^{9} c_{1} \textit {\_Z}^{72}-65610 \left (5 x -11\right )^{9} c_{1} \textit {\_Z}^{63}-375435 \left (5 x -11\right )^{9} c_{1} \textit {\_Z}^{54}+115911 \left (5 x -11\right )^{9} c_{1} \textit {\_Z}^{45}+166860 \left (5 x -11\right )^{9} c_{1} \textit {\_Z}^{36}-12960 \left (5 x -11\right )^{9} c_{1} \textit {\_Z}^{27}-40320 \left (5 x -11\right )^{9} c_{1} \textit {\_Z}^{18}-11520 \left (5 x -11\right )^{9} c_{1} \textit {\_Z}^{9}-1024 \left (5 x -11\right )^{9} c_{1}\right )^{9}-1\right )}{5 \RootOf \left (59049 \left (5 x -11\right )^{9} c_{1} \textit {\_Z}^{90}+\left (-295245 \left (5 x -11\right )^{9} c_{1}+1\right ) \textit {\_Z}^{81}+459270 \left (5 x -11\right )^{9} c_{1} \textit {\_Z}^{72}-65610 \left (5 x -11\right )^{9} c_{1} \textit {\_Z}^{63}-375435 \left (5 x -11\right )^{9} c_{1} \textit {\_Z}^{54}+115911 \left (5 x -11\right )^{9} c_{1} \textit {\_Z}^{45}+166860 \left (5 x -11\right )^{9} c_{1} \textit {\_Z}^{36}-12960 \left (5 x -11\right )^{9} c_{1} \textit {\_Z}^{27}-40320 \left (5 x -11\right )^{9} c_{1} \textit {\_Z}^{18}-11520 \left (5 x -11\right )^{9} c_{1} \textit {\_Z}^{9}-1024 \left (5 x -11\right )^{9} c_{1}\right )^{9}} \]
✓ Solution by Mathematica
Time used: 93.585 (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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