62.12.5 problem Ex 5

Internal problem ID [12851]
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
Date solved : Tuesday, January 28, 2025 at 04:27:19 AM
CAS classification : [_Bernoulli]

\begin{align*} x y^{\prime }+y+x^{4} y^{4} {\mathrm e}^{x}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 62

dsolve(x*diff(y(x),x)+y(x)+x^4*y(x)^4*exp(x)=0,y(x), singsol=all)
 

\begin{align*} y &= \frac {1}{\left (3 \,{\mathrm e}^{x}+c_{1} \right )^{{1}/{3}} x} \\ y &= -\frac {1+i \sqrt {3}}{2 \left (3 \,{\mathrm e}^{x}+c_{1} \right )^{{1}/{3}} x} \\ y &= \frac {i \sqrt {3}-1}{2 \left (3 \,{\mathrm e}^{x}+c_{1} \right )^{{1}/{3}} x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 11.387 (sec). Leaf size: 79

DSolve[x*D[y[x],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*}