Internal problem ID [3051]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 11
Problem number: 303.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\left (x^{2}+1\right ) y^{\prime }-1-x^{2}+y \,\mathrm {arccot}\relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve((x^2+1)*diff(y(x),x) = 1+x^2-y(x)*arccot(x),y(x), singsol=all)
\[ y \relax (x ) = \left (\int {\mathrm e}^{-\frac {\mathrm {arccot}\relax (x )^{2}}{2}}d x +c_{1}\right ) {\mathrm e}^{\frac {\mathrm {arccot}\relax (x )^{2}}{2}} \]
✓ Solution by Mathematica
Time used: 2.601 (sec). Leaf size: 37
DSolve[(1+x^2)y'[x]==(1+x^2)-y[x] ArcCot[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{\frac {1}{2} \cot ^{-1}(x)^2} \left (\int _1^xe^{-\frac {1}{2} \cot ^{-1}(K[1])^2}dK[1]+c_1\right ) \\ \end{align*}