29.31.24 problem 924

Internal problem ID [5503]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 31
Problem number : 924
Date solved : Monday, January 27, 2025 at 11:32:59 AM
CAS classification : [_linear]

\begin{align*} 4 x^{2} {y^{\prime }}^{2}-4 x y y^{\prime }&=8 x^{3}-y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.049 (sec). Leaf size: 30

dsolve(4*x^2*diff(y(x),x)^2-4*x*y(x)*diff(y(x),x) = 8*x^3-y(x)^2,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.084 (sec). Leaf size: 42

DSolve[4 x^2 (D[y[x],x])^2-4 x y[x] D[y[x],x]==8 x^3 -y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

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