75.4.1 problem 46

Internal problem ID [16703]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 4. Equations with variables separable and equations reducible to them. Exercises page 38
Problem number : 46
Date solved : Tuesday, January 28, 2025 at 09:18:45 AM
CAS classification : [_separable]

\begin{align*} 1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 11

dsolve((1+y(x)^2)+(1+x^2)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = -\tan \left (\arctan \left (x \right )+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.343 (sec). Leaf size: 57

DSolve[(1+y[x]^2)+(1+x^2)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{K[1]^2+1}dK[1]\&\right ]\left [\int _1^x-\frac {1}{K[2]^2+1}dK[2]+c_1\right ] \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}