Internal problem ID [7909]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 329.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational]
Solve \begin {gather*} \boxed {y^{m} x^{n} \left (y^{\prime } a x +b y\right )+\alpha x y^{\prime }+\beta y=0} \end {gather*}
✓ Solution by Maple
Time used: 1.172 (sec). Leaf size: 78
dsolve(y(x)^m*x^n*(a*x*diff(y(x),x)+b*y(x))+alpha*x*diff(y(x),x)+beta*y(x) = 0,y(x), singsol=all)
\[ x^{a \beta m n -b \beta \,m^{2}} \left (x^{n} n y \relax (x )^{m} a -x^{n} y \relax (x )^{m} m b +\alpha n -\beta m \right )^{-a \beta m +b m \alpha } \left (y \relax (x )^{m}\right )^{a n \alpha -b m \alpha }-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.911 (sec). Leaf size: 119
DSolve[\[Beta]*y[x] + \[Alpha]*x*y'[x] + x^n*y[x]^m*(b*y[x] + a*x*y'[x])==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {m \left (\beta (b m-a n) \log \left (n x^n (\alpha n-\beta m)\right )+n (a \beta -\alpha b) \log \left (x^n y(x)^m (b m-a n)+\beta m-\alpha n\right )\right )}{n (a n-b m) (\alpha n-\beta m)}-\frac {\alpha m \log (\alpha n y(x)-\beta m y(x))}{\alpha n-\beta m}=c_1,y(x)\right ] \]