31.14 problem 913

Internal problem ID [4149]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 31
Problem number: 913.
ODE order: 1.
ODE degree: 2.

CAS Maple gives this as type [_quadrature]

\[ \boxed {x^{2} {y^{\prime }}^{2}+\left (a +b \,x^{2} y^{3}\right ) y^{\prime }+a b y^{3}=0} \]

Solution by Maple

Time used: 0.0 (sec). Leaf size: 35

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

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

Solution by Mathematica

Time used: 0.065 (sec). Leaf size: 49

DSolve[x^2 (y'[x])^2+(a+b x^2 y[x]^3)y'[x]+a b y[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{\sqrt {2 b x-2 c_1}} y(x)\to \frac {1}{\sqrt {2 b x-2 c_1}} y(x)\to \frac {a}{x}+c_1 \end{align*}