Internal problem ID [3598]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 30
Problem number: 869.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class G]]
Solve \begin {gather*} \boxed {x \left (y^{\prime }\right )^{2}-3 y y^{\prime }+9 x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.13 (sec). Leaf size: 43
dsolve(x*diff(y(x),x)^2-3*y(x)*diff(y(x),x)+9*x^2 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {4 x^{3}+c_{1}^{2}}{2 c_{1}} \\ y \relax (x ) = \frac {c_{1}^{2} x^{3}+4}{2 c_{1}} \\ y \relax (x ) = c_{1} x^{\frac {3}{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.301 (sec). Leaf size: 79
DSolve[x (y'[x])^2-3 y[x] y'[x]+9 x^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{2} e^{-\frac {3 c_1}{2}} \left (4 x^3+e^{3 c_1}\right ) \\ y(x)\to \frac {1}{2} e^{-\frac {3 c_1}{2}} \left (4 x^3+e^{3 c_1}\right ) \\ y(x)\to -2 x^{3/2} \\ y(x)\to 2 x^{3/2} \\ \end{align*}