60.2.404 problem 981

Internal problem ID [10991]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 981
Date solved : Monday, January 27, 2025 at 10:38:56 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], _Abel]

\begin{align*} y^{\prime }&=\frac {y^{3} a^{3} x^{3}+3 y^{2} a^{2} x^{2}+3 a x y+1+a^{2} x}{x^{3} a^{3}} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 41

dsolve(diff(y(x),x) = (y(x)^3*a^3*x^3+3*y(x)^2*a^2*x^2+3*y(x)*a*x+1+a^2*x)/x^3/a^3,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.278 (sec). Leaf size: 61

DSolve[D[y[x],x] == (1 + a^2*x + 3*a*x*y[x] + 3*a^2*x^2*y[x]^2 + a^3*x^3*y[x]^3)/(a^3*x^3),y[x],x,IncludeSingularSolutions -> True]
 

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