60.1.327 problem 328

Internal problem ID [10341]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 328
Date solved : Monday, January 27, 2025 at 07:17:23 PM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} a \,x^{2} y^{n} y^{\prime }-2 x y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.277 (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)
 

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

✓ Solution by Mathematica

Time used: 0.554 (sec). Leaf size: 170

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

\[ \text {Solve}\left [\int _1^{y(x)}\left (\frac {n \left (a x K[2]^n-2\right )}{K[2] \left (-a x K[2]^n+n+2\right )}-\int _1^x\left (\frac {a^2 n^2 K[1] K[2]^{2 n-1}}{(n+2) \left (a K[1] K[2]^n-n-2\right )^2}-\frac {a n^2 K[2]^{n-1}}{(n+2) \left (a K[1] K[2]^n-n-2\right )}\right )dK[1]\right )dK[2]+\int _1^x\left (\frac {n}{(n+2) K[1]}-\frac {a n y(x)^n}{(n+2) \left (a K[1] y(x)^n-n-2\right )}\right )dK[1]=c_1,y(x)\right ] \]