Internal problem ID [11674]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]
\[ \boxed {y^{\prime }+8 y^{2} x -4 x \left (4 x +1\right ) y=-8 x^{3}-4 x^{2}+1} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = \frac {c_{1} \left (2 x +1\right ) {\mathrm e}^{\frac {8}{3} x^{3}+2 x^{2}}+2 \,{\mathrm e}^{\frac {8 x^{3}}{3}} x}{2 c_{1} {\mathrm e}^{\frac {8}{3} x^{3}+2 x^{2}}+2 \,{\mathrm e}^{\frac {8 x^{3}}{3}}} \]
✓ Solution by Mathematica
Time used: 0.196 (sec). Leaf size: 30
DSolve[y'[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*}