83.8.12 problem 13

Internal problem ID [19138]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Misc examples on chapter II at page 25
Problem number : 13
Date solved : Tuesday, January 28, 2025 at 01:05:12 PM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Solution by Maple

Time used: 0.148 (sec). Leaf size: 33

dsolve(y(x)+(a*x^2*y(x)^n-2*x)*diff(y(x),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: 0.199 (sec). Leaf size: 42

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

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