75.4.4 problem 49

Internal problem ID [16706]
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 : 49
Date solved : Tuesday, January 28, 2025 at 09:18:53 AM
CAS classification : [_separable]

\begin{align*} 1+y^{2}&=x y^{\prime } \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 9

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

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

✓ Solution by Mathematica

Time used: 0.242 (sec). Leaf size: 42

DSolve[(1+y[x]^2)==x*D[y[x],x],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 ][\log (x)+c_1] \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}