56.1.14 problem 14

Internal problem ID [8726]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 14
Date solved : Monday, January 27, 2025 at 04:20:46 PM
CAS classification : [_separable]

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

✓ 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)
 

\[ \int \frac {1}{\ln \left (x^{2}+1\right )}d x -\int _{}^{y}\frac {1}{\ln \left (\textit {\_a}^{2}+1\right )}d \textit {\_a} +c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.688 (sec). Leaf size: 48

DSolve[D[y[x],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*}