Internal problem ID [10161]
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 19. Summary.
Page 29
Problem number: Ex 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime } x +y+{\mathrm e}^{x} x^{4} y^{4}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 80
dsolve(x*diff(y(x),x)+y(x)+x^4*y(x)^4*exp(x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {1}{\left (3 \,{\mathrm e}^{x}+c_{1}\right )^{\frac {1}{3}} x} \\ y \relax (x ) = \frac {-\frac {1}{2 \left (3 \,{\mathrm e}^{x}+c_{1}\right )^{\frac {1}{3}}}-\frac {i \sqrt {3}}{2 \left (3 \,{\mathrm e}^{x}+c_{1}\right )^{\frac {1}{3}}}}{x} \\ y \relax (x ) = \frac {-\frac {1}{2 \left (3 \,{\mathrm e}^{x}+c_{1}\right )^{\frac {1}{3}}}+\frac {i \sqrt {3}}{2 \left (3 \,{\mathrm e}^{x}+c_{1}\right )^{\frac {1}{3}}}}{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 10.69 (sec). Leaf size: 79
DSolve[x*y'[x]+y[x]+x^4*y[x]^4*Exp[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{\sqrt [3]{x^3 \left (3 e^x+c_1\right )}} \\ y(x)\to -\frac {\sqrt [3]{-1}}{\sqrt [3]{x^3 \left (3 e^x+c_1\right )}} \\ y(x)\to \frac {(-1)^{2/3}}{\sqrt [3]{x^3 \left (3 e^x+c_1\right )}} \\ y(x)\to 0 \\ \end{align*}