Internal problem ID [494]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.2. Page 48
Problem number: 16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x \left (x^{2}+1\right )}{4 y^{3}}=0} \end {gather*} With initial conditions \begin {align*} \left [y \relax (0) = -\frac {\sqrt {2}}{2}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.062 (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)
\[ y \relax (x ) = -\frac {\sqrt {2 x^{2}+2}}{2} \]
✓ Solution by Mathematica
Time used: 0.251 (sec). Leaf size: 23
DSolve[{y'[x] == 1/4*x*(x^2+1)/y[x]^3,y[0]==-(1/Sqrt[2])},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt [4]{\left (x^2+1\right )^2}}{\sqrt {2}} \\ \end{align*}