12.9.46 problem 39 part(d)

Internal problem ID [1802]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 5 linear second order equations. Section 5.6 Reduction or order. Page 253
Problem number : 39 part(d)
Date solved : Monday, January 27, 2025 at 05:35:15 AM
CAS classification : [_rational, _Riccati]

\begin{align*} \left (3 x -1\right ) \left (y^{\prime }+y^{2}\right )-\left (3 x +2\right ) y-6 x +8&=0 \end{align*}

✓ Solution by Maple

Time used: 0.038 (sec). Leaf size: 31

dsolve((3*x-1)*(diff(y(x),x)+y(x)^2)-(3*x+2)*y(x)-6*x+8=0,y(x), singsol=all)
 

\[ y = \frac {-c_1 x +2 \,{\mathrm e}^{3 x -1}+c_1}{c_1 x +{\mathrm e}^{3 x -1}} \]

✓ Solution by Mathematica

Time used: 0.449 (sec). Leaf size: 41

DSolve[(3*x-1)*(D[y[x],x]+y[x]^2)-(3*x+2)*y[x]-6*x+8==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {2 \left (-e x+c_1 e^{3 x}+e\right )}{2 e x+c_1 e^{3 x}} \\ y(x)\to 2 \\ \end{align*}