15.19.7 problem 7

Internal problem ID [3291]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 37, page 171
Problem number : 7
Date solved : Monday, January 27, 2025 at 07:31:20 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 49

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

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

✓ Solution by Mathematica

Time used: 0.157 (sec). Leaf size: 80

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

\begin{align*} y(x)\to -\sqrt {2} \sqrt {-x^2+c_1} \\ y(x)\to \sqrt {2} \sqrt {-x^2+c_1} \\ y(x)\to -\sqrt {x^2+2 c_1} \\ y(x)\to \sqrt {x^2+2 c_1} \\ \end{align*}