40.2.25 problem 51

Internal problem ID [6603]
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
Date solved : Monday, January 27, 2025 at 02:15:29 PM
CAS classification : [[_homogeneous, `class C`], _Riccati]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 24

dsolve(diff(y(x),x)= -2*(2*x+3*y(x))^2,y(x), singsol=all)
 

\[ y = -\frac {2 x}{3}-\frac {\sqrt {3}\, \tanh \left (2 \left (-x +c_1 \right ) \sqrt {3}\right )}{9} \]

✓ Solution by Mathematica

Time used: 0.164 (sec). Leaf size: 59

DSolve[D[y[x],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*}