Internal problem ID [5260]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 4. Equations of first order and first degree (Variable separable). Supplemetary
problems. Page 22
Problem number: 51.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _Riccati]
\[ \boxed {y^{\prime }+2 \left (3 y+2 x \right )^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(diff(y(x),x)= -2*(2*x+3*y(x))^2,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {2 x}{3}-\frac {\sqrt {3}\, \tanh \left (2 \left (-x +c_{1} \right ) \sqrt {3}\right )}{9} \]
✓ Solution by Mathematica
Time used: 0.142 (sec). Leaf size: 59
DSolve[y'[x]==-2*(2*x+3*y[x])^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{9} \left (-6 x-\frac {6}{\sqrt {3}+12 c_1 e^{4 \sqrt {3} x}}+\sqrt {3}\right ) \\ y(x)\to \frac {1}{9} \left (\sqrt {3}-6 x\right ) \\ \end{align*}