29.31.14 problem 913

Internal problem ID [5493]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 31
Problem number : 913
Date solved : Monday, January 27, 2025 at 11:31:36 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.006 (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 {1}{\sqrt {2 b x +c_{1}}} \\ y \left (x \right ) &= -\frac {1}{\sqrt {2 b x +c_{1}}} \\ y \left (x \right ) &= \frac {a}{x}+c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.075 (sec). Leaf size: 49

DSolve[x^2 (D[y[x],x])^2+(a+b x^2 y[x]^3)D[y[x],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*}