83.34.4 problem 4

Internal problem ID [19417]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Exercise VII (H) at page 118
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 01:38:51 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }&=\sqrt {m \,x^{2} {y^{\prime }}^{3}+n y^{2}} \end{align*}

✗ Solution by Maple

dsolve(x^2*diff(y(x),x$2)=sqrt(m*x^2*diff(y(x),x)^3+n*y(x)^2),y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[x^2*D[y[x],{x,2}]==Sqrt[m*x^2*D[y[x],x]^3+n*y[x]^2],y[x],x,IncludeSingularSolutions -> True]
 

Not solved