Internal problem ID [589]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Miscellaneous problems, end of chapter 2. Page 133
Problem number: 22.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x^{2}-1}{1+y^{2}}=0} \end {gather*} With initial conditions \begin {align*} [y \left (-1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.132 (sec). Leaf size: 87
dsolve([diff(y(x),x) = (x^2-1)/(1+y(x)^2),y(-1) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (8+4 x^{3}-12 x +4 \sqrt {x^{6}-6 x^{4}+4 x^{3}+9 x^{2}-12 x +8}\right )^{\frac {2}{3}}-4}{2 \left (8+4 x^{3}-12 x +4 \sqrt {x^{6}-6 x^{4}+4 x^{3}+9 x^{2}-12 x +8}\right )^{\frac {1}{3}}} \]
✓ Solution by Mathematica
Time used: 2.859 (sec). Leaf size: 85
DSolve[{y'[x]== (x^2-1)/(1+y[x]^2),y[-1]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt [3]{2} \left (x^3+\sqrt {x \left (x^2-3\right ) \left (x^3-3 x+4\right )+8}-3 x+2\right )^{2/3}-2}{2^{2/3} \sqrt [3]{x^3+\sqrt {x \left (x^2-3\right ) \left (x^3-3 x+4\right )+8}-3 x+2}} \\ \end{align*}