83.22.17 problem 17

Internal problem ID [19271]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter IV. Equations of the first order but not of the first degree. Exercise IV (E) at page 63
Problem number : 17
Date solved : Tuesday, January 28, 2025 at 01:19:05 PM
CAS classification : [_separable]

\begin{align*} x y {y^{\prime }}^{2}+y^{\prime } \left (3 x^{2}-2 y^{2}\right )-6 y x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 35

dsolve(x*y(x)*diff(y(x),x)^2+diff(y(x),x)*(3*x^2-2*y(x)^2)-6*x*y(x)=0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= c_{1} x^{2} \\ y \left (x \right ) &= \sqrt {-3 x^{2}+c_{1}} \\ y \left (x \right ) &= -\sqrt {-3 x^{2}+c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.143 (sec). Leaf size: 54

DSolve[x*y[x]*D[y[x],x]^2+D[y[x],x]*(3*x^2-2*y[x]^2)-6*x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 x^2 \\ y(x)\to -\sqrt {-3 x^2+2 c_1} \\ y(x)\to \sqrt {-3 x^2+2 c_1} \\ y(x)\to 0 \\ \end{align*}