29.33.30 problem 993

Internal problem ID [5569]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 33
Problem number : 993
Date solved : Monday, January 27, 2025 at 12:06:41 PM
CAS classification : [_separable]

\begin{align*} 4 y^{2} {y^{\prime }}^{2}+2 \left (1+3 x \right ) x y y^{\prime }+3 x^{3}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 59

dsolve(4*y(x)^2*diff(y(x),x)^2+2*(1+3*x)*x*y(x)*diff(y(x),x)+3*x^3 = 0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= -\frac {\sqrt {-2 x^{2}+4 c_{1}}}{2} \\ y \left (x \right ) &= \frac {\sqrt {-2 x^{2}+4 c_{1}}}{2} \\ y \left (x \right ) &= \sqrt {-x^{3}+c_{1}} \\ y \left (x \right ) &= -\sqrt {-x^{3}+c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.155 (sec). Leaf size: 81

DSolve[4 y[x]^2 (D[y[x],x])^2 +2(1+3 x)x y[x] D[y[x],x]+3 x^3==0,y[x],x,IncludeSingularSolutions -> True]
 

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