64.5.37 problem 41

Internal problem ID [13350]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.3 (Linear equations). Exercises page 56
Problem number : 41
Date solved : Tuesday, January 28, 2025 at 05:31:26 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]

\begin{align*} y^{\prime }&=-8 x y^{2}+4 x \left (4 x +1\right ) y-8 x^{3}-4 x^{2}+1 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 60

dsolve(diff(y(x),x)=-8*x*y(x)^2+4*x*(4*x+1)*y(x)-(8*x^3+4*x^2-1),y(x), singsol=all)
 

\[ y = \frac {c_{1} \left (2 x +1\right ) {\mathrm e}^{\frac {8}{3} x^{3}+2 x^{2}}+2 \,{\mathrm e}^{\frac {8 x^{3}}{3}} x}{2 c_{1} {\mathrm e}^{\frac {8}{3} x^{3}+2 x^{2}}+2 \,{\mathrm e}^{\frac {8 x^{3}}{3}}} \]

✓ Solution by Mathematica

Time used: 0.216 (sec). Leaf size: 30

DSolve[D[y[x],x]==-8*x*y[x]^2+4*x*(4*x+1)*y[x]-(8*x^3+4*x^2-1),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{4} \left (\tanh \left (x^2+i c_1\right )+4 x+1\right ) \\ y(x)\to \text {Indeterminate} \\ \end{align*}