Internal problem ID [7030]
Book: Selected problems from homeworks from different courses
Section: Math 2520, summer 2021. Differential Equations and Linear Algebra. Normandale
college, Bloomington, Minnesota
Problem number: HW 1 problem 6(b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (x^{2}+1\right ) y^{\prime }+y^{2}=-1} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 11
dsolve([(x^2+1)*diff(y(x),x)+y(x)^2=-1,y(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \cot \left (\arctan \left (x \right )+\frac {\pi }{4}\right ) \]
✓ Solution by Mathematica
Time used: 0.264 (sec). Leaf size: 14
DSolve[{(x^2+1)*y'[x]+y[x]^2==-1,{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \cot \left (\arctan (x)+\frac {\pi }{4}\right ) \]