1.327 problem 328

Internal problem ID [8664]

Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 328.
ODE order: 1.
ODE degree: 1.

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

\[ \boxed {a \,x^{2} y^{n} y^{\prime }-2 x y^{\prime }+y=0} \]

Solution by Maple

Time used: 0.234 (sec). Leaf size: 33

dsolve(a*x^2*y(x)^n*diff(y(x),x)-2*x*diff(y(x),x)+y(x) = 0,y(x), singsol=all)
 

\[ \left (y \left (x \right )^{n} a x -n -2\right )^{n} y \left (x \right )^{2 n} x^{-n}-c_{1} = 0 \]

Solution by Mathematica

Time used: 0.21 (sec). Leaf size: 42

DSolve[y[x] - 2*x*y'[x] + a*x^2*y[x]^n*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

\[ \text {Solve}\left [\frac {n \left (\log (x)-\log \left (-a x y(x)^n+n+2\right )\right )}{n+2}-\frac {2 n \log (y(x))}{n+2}=c_1,y(x)\right ] \]