Internal problem ID [10137]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 14. Equations
reducible to linear equations (Bernoulli). Page 21
Problem number: Ex 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {4 y^{\prime } x +3 y+{\mathrm e}^{x} x^{4} y^{5}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 75
dsolve(4*x*diff(y(x),x)+3*y(x)+exp(x)*x^4*y(x)^5=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {1}{\sqrt {\sqrt {x \,{\mathrm e}^{x}+x c_{1}}\, x}} \\ y \relax (x ) = \frac {1}{\sqrt {-\sqrt {x \,{\mathrm e}^{x}+x c_{1}}\, x}} \\ y \relax (x ) = -\frac {1}{\sqrt {\sqrt {x \,{\mathrm e}^{x}+x c_{1}}\, x}} \\ y \relax (x ) = -\frac {1}{\sqrt {-\sqrt {x \,{\mathrm e}^{x}+x c_{1}}\, x}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 14.248 (sec). Leaf size: 88
DSolve[4*x*y'[x]+3*y[x]+Exp[x]*x^4*y[x]^5==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{\sqrt [4]{x^3 \left (e^x+c_1\right )}} \\ y(x)\to -\frac {i}{\sqrt [4]{x^3 \left (e^x+c_1\right )}} \\ y(x)\to \frac {i}{\sqrt [4]{x^3 \left (e^x+c_1\right )}} \\ y(x)\to \frac {1}{\sqrt [4]{x^3 \left (e^x+c_1\right )}} \\ y(x)\to 0 \\ \end{align*}