15.21.10 problem 32

Internal problem ID [3334]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 39, page 179
Problem number : 32
Date solved : Monday, January 27, 2025 at 07:34:24 AM
CAS classification : [_separable]

\begin{align*} y^{2}-2 x y y^{\prime }+{y^{\prime }}^{2} \left (x^{2}-1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 17

dsolve(y(x)^2-2*diff(y(x),x)*x*y(x)+diff(y(x),x)^2*(x^2-1)=0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= c_{1} \left (x -1\right ) \\ y \left (x \right ) &= \left (x +1\right ) c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.048 (sec). Leaf size: 26

DSolve[y[x]^2-2*D[y[x],x]*x*y[x]+D[y[x],x]^2*(x^2-1)==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 (x-1) \\ y(x)\to c_1 (x+1) \\ y(x)\to 0 \\ \end{align*}