Internal problem ID [6305]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 14.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {\ln \left (1+y^{2}\right )}{\ln \left (x^{2}+1\right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 30
dsolve(diff(y(x),x)=ln(y(x)^2+1)/ln(x^2+1),y(x), singsol=all)
\[ \int \frac {1}{\ln \left (x^{2}+1\right )}d x -\left (\int _{}^{y \relax (x )}\frac {1}{\ln \left (\textit {\_a}^{2}+1\right )}d \textit {\_a} \right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.59 (sec). Leaf size: 48
DSolve[y'[x] == Log[1+y[x]^2]/Log[1+x^2],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{\log \left (K[1]^2+1\right )}dK[1]\&\right ]\left [\int _1^x\frac {1}{\log \left (K[2]^2+1\right )}dK[2]+c_1\right ] \\ y(x)\to 0 \\ \end{align*}