Internal problem ID [4225]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 33
Problem number: 993.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_separable]
\[ \boxed {4 y^{2} {y^{\prime }}^{2}+2 \left (1+3 x \right ) x y y^{\prime }=-3 x^{3}} \]
✓ Solution by Maple
Time used: 0.015 (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: 0.169 (sec). Leaf size: 81
DSolve[4 y[x]^2 (y'[x])^2 +2(1+3 x)x y[x] y'[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*}