10.2.16 problem 16

Internal problem ID [1144]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 16
Date solved : Monday, January 27, 2025 at 04:35:43 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {x \left (x^{2}+1\right )}{4 y^{3}} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-\frac {\sqrt {2}}{2} \end{align*}

✓ Solution by Maple

Time used: 0.051 (sec). Leaf size: 15

dsolve([diff(y(x),x) = 1/4*x*(x^2+1)/y(x)^3,y(0) = -1/2*2^(1/2)],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.219 (sec). Leaf size: 23

DSolve[{D[y[x],x] == 1/4*x*(x^2+1)/y[x]^3,y[0]==-(1/Sqrt[2])},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {\sqrt [4]{\left (x^2+1\right )^2}}{\sqrt {2}} \]