12.5.13 problem 9

Internal problem ID [1637]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable Equations. Section 2.4 Page 68
Problem number : 9
Date solved : Monday, January 27, 2025 at 05:15:29 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

With initial conditions

\begin{align*} y \left (1\right )&={\frac {1}{2}} \end{align*}

✓ Solution by Maple

Time used: 0.069 (sec). Leaf size: 34

dsolve([x*diff(y(x),x)+y(x)=x^4*y(x)^4,y(1) = 1/2],y(x), singsol=all)
 

\[ y = \frac {\left (-\left (3 x -11\right )^{2}\right )^{{1}/{3}} \left (i \sqrt {3}-1\right )}{6 x^{2}-22 x} \]

✓ Solution by Mathematica

Time used: 0.613 (sec). Leaf size: 19

DSolve[{x*D[y[x],x]+y[x]==x^4*y[x]^4,y[1]==1/2},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{\sqrt [3]{-x^3 (3 x-11)}} \]