83.34.3 problem 3

Internal problem ID [19416]
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 : 3
Date solved : Tuesday, January 28, 2025 at 08:32:45 PM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]

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

✓ Solution by Maple

Time used: 0.028 (sec). Leaf size: 23

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

\begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= \frac {x \left (2 c_{2} \ln \left (x \right )+c_{1} \right )^{2}}{4 c_{2}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.220 (sec). Leaf size: 17

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

\begin{align*} y(x)\to c_2 x \\ y(x)\to c_2 x \\ \end{align*}