60.1.442 problem 445

Internal problem ID [10456]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 445
Date solved : Monday, January 27, 2025 at 07:46:04 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 35

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

\begin{align*} y &= \frac {1}{\sqrt {2 a x +c_{1}}} \\ y &= -\frac {1}{\sqrt {2 a x +c_{1}}} \\ y &= \frac {b}{x}+c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.070 (sec). Leaf size: 49

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

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