62.7.4 problem Ex 4

Internal problem ID [12827]
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
Date solved : Tuesday, January 28, 2025 at 04:25:40 AM
CAS classification : [_Bernoulli]

\begin{align*} 4 x y^{\prime }+3 y+{\mathrm e}^{x} x^{4} y^{5}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.060 (sec). Leaf size: 67

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

✓ Solution by Mathematica

Time used: 15.152 (sec). Leaf size: 88

DSolve[4*x*D[y[x],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*}