15.5.16 problem 20

Internal problem ID [2952]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 9, page 38
Problem number : 20
Date solved : Monday, January 27, 2025 at 07:00:23 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.038 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

Time used: 0.510 (sec). Leaf size: 21

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

\[ y(x)\to -\frac {1}{\sqrt {-x^2 \left (x^2-2\right )}} \]