Internal problem ID [1053]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Exact equations. Section 2.5 Page 79
Problem number: 24.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _Bernoulli]
Solve \begin {gather*} \boxed {{\mathrm e}^{x} \left (y^{2} x^{4}+4 x^{3} y^{2}+1\right )+\left (2 x^{4} y \,{\mathrm e}^{x}+2 y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 66
dsolve((exp(x)*(x^4*y(x)^2+4*x^3*y(x)^2+1))+(2*x^4*y(x)*exp(x)+2*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {-\left ({\mathrm e}^{x} x^{4}+1\right ) \left (-c_{1}+{\mathrm e}^{x}\right )}}{{\mathrm e}^{x} x^{4}+1} \\ y \relax (x ) = -\frac {\sqrt {-\left ({\mathrm e}^{x} x^{4}+1\right ) \left (-c_{1}+{\mathrm e}^{x}\right )}}{{\mathrm e}^{x} x^{4}+1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.072 (sec). Leaf size: 62
DSolve[(Exp[x]*(x^4*y[x]^2+4*x^3*y[x]^2+1))+(2*x^4*y[x]*Exp[x]+2*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {-e^x+c_1}}{\sqrt {e^x x^4+1}} \\ y(x)\to \frac {\sqrt {-e^x+c_1}}{\sqrt {e^x x^4+1}} \\ \end{align*}