29.33.5 problem 967

Internal problem ID [5544]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 33
Problem number : 967
Date solved : Monday, January 27, 2025 at 11:43:22 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 35

dsolve(x*y(x)*diff(y(x),x)^2+(3*x^2-2*y(x)^2)*diff(y(x),x)-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: 0.139 (sec). Leaf size: 54

DSolve[x y[x] (D[y[x],x])^2+(3 x^2-2 y[x]^2)D[y[x],x]-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*}