15.4.4 problem 4

Internal problem ID [2917]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 8, page 34
Problem number : 4
Date solved : Monday, January 27, 2025 at 06:55:43 AM
CAS classification : [_exact, _rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]

\begin{align*} x \left (6 y x +5\right )+\left (2 x^{3}+3 y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 55

dsolve(x*(6*x*y(x)+5)+(2*x^3+3*y(x))*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= -\frac {2 x^{3}}{3}-\frac {\sqrt {4 x^{6}-15 x^{2}-6 c_1}}{3} \\ y &= -\frac {2 x^{3}}{3}+\frac {\sqrt {4 x^{6}-15 x^{2}-6 c_1}}{3} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.159 (sec). Leaf size: 69

DSolve[x*(6*x*y[x]+5)+(2*x^3+3*y[x])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{3} \left (-2 x^3-\sqrt {4 x^6-15 x^2+9 c_1}\right ) \\ y(x)\to \frac {1}{3} \left (-2 x^3+\sqrt {4 x^6-15 x^2+9 c_1}\right ) \\ \end{align*}