44.5.28 problem 28

Internal problem ID [7090]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 28
Date solved : Tuesday, January 28, 2025 at 08:48:42 PM
CAS classification : [_separable]

\begin{align*} \left (x^{4}+1\right ) y^{\prime }+x \left (1+4 y^{2}\right )&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.057 (sec). Leaf size: 21

dsolve([(1+x^4)*diff(y(x),x)+x*(1+4*y(x)^2)=0,y(1) = 0],y(x), singsol=all)
 

\[ y = \frac {-x^{2}+1}{2 x^{2}+2} \]

✓ Solution by Mathematica

Time used: 0.296 (sec). Leaf size: 20

DSolve[{(1+x^4)*D[y[x],x]+x*(1+4*y[x]^2)==0,{y[1]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} \cot \left (\arctan \left (x^2\right )+\frac {\pi }{4}\right ) \]