29.11.12 problem 303

Internal problem ID [4903]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 11
Problem number : 303
Date solved : Monday, January 27, 2025 at 09:47:22 AM
CAS classification : [_linear]

\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=1+x^{2}-y \,\operatorname {arccot}\left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 23

dsolve((x^2+1)*diff(y(x),x) = 1+x^2-y(x)*arccot(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \left (\int {\mathrm e}^{-\frac {\operatorname {arccot}\left (x \right )^{2}}{2}}d x +c_{1} \right ) {\mathrm e}^{\frac {\operatorname {arccot}\left (x \right )^{2}}{2}} \]

✓ Solution by Mathematica

Time used: 3.489 (sec). Leaf size: 37

DSolve[(1+x^2)D[y[x],x]==(1+x^2)-y[x] ArcCot[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{\frac {1}{2} \cot ^{-1}(x)^2} \left (\int _1^xe^{-\frac {1}{2} \cot ^{-1}(K[1])^2}dK[1]+c_1\right ) \]